control parameter estimation in a semi linear parabolic inverse problem using a high accurate method abstract parabolic inverse problems have an important role in many branches of science and technology the aim of this research work is to solve these classes of equations using a high order compact finite difference scheme we consider the following inverse problem for finding u x t and p t governed by u t u xx p t u x t with an over specified condition inside the domain spatial derivatives are approximated using central difference scheme the time advancement of the simulation is performed using a third order compact runge kutta method the convergence orders for the approximation of both u and p are of o k 3 h 2 which improves the results obtained in the literature an exact test case is used to evaluate the validity of our numerical analysis we found that the accuracy of the results is better than that of previous works in the literature

a splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problem one of the global approaches for solving the two dimensional inverse parabolic problem is the predictor corrector which takes place for evaluating the pair u p and adjusting the evaluation for the desired accuracy for general class of higher dimensional parabolic problems the adi or the fs methods have been considered with an advantage of reducing or splitting the problem in accordance to the time fractions into one dimensional dependent problems and they are a non parallel type of splittings in 1992 lu et al proposed an additive parallel type of splitting method such that the splitting is defined in accordance to the spatial variables to solve multi dimensional parabolic problem in this work we will present a new algorithm for solving two or higher dimensional inverse control problem the algorithm is a parallel predictor corrector type of method such that the solution and the predictor and corrector schemes are defined by the parallel splitting up method some numerical results from the solution of two model problems are considered to demonstrate the accuracy of the presented algorithm

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

error and extrapolation of a compact lod method for parabolic differential equations this paper is concerned with a compact locally one dimensional lod finite difference method for solving two dimensional nonhomogeneous parabolic differential equations an explicit error estimate for the finite difference solution is given in the discrete infinity norm it is shown that the method has the accuracy of the second order in time and the fourth order in space with respect to the discrete infinity norm a richardson extrapolation algorithm is developed to make the final computed solution fourth order accurate in both time and space when the time step equals the spatial mesh size numerical results demonstrate the accuracy and the high efficiency of the extrapolation algorithm

a higher order compact adi method with monotone iterative procedure for systems of reaction diffusion equations this paper is concerned with an existing compact finite difference adi method published in the paper by liao et al 2002 3 for solving systems of two dimensional reaction diffusion equations with nonlinear reaction terms this method has an accuracy of fourth order in space and second order in time the existence and uniqueness of its solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear reaction terms the convergence of the finite difference solution to the continuous solution is proved an efficient monotone iterative algorithm is presented for solving the resulting discrete system and some techniques for the construction of upper and lower solutions are discussed an application using a model problem gives numerical results that demonstrate the high efficiency and advantages of the method

optimal power control for ldpc codes in block fading channels we study the error probability of ldpc codes in delay limited block fading channels with channel state information csi at the transmitter and the receiver we derive the optimal power allocation algorithms for ldpc codes with specific degree distributions using multi edge type density evolution error boundaries the resulting performance approaches the outage probability for a number of power constraints furthermore we adapt the algorithm for finite length codes and show that the proposed algorithm enables gains larger than 10 db over uniform power allocation the method is valid for general possibly correlated fading distributions this represents the first analysis of specific ldpc codes over block fading channels with full csi

stability of numerical methods for delay differential equations abstract consider the following delay differential equation dde y t y t y t t t t 0 with the initial condition y t for t t 0 where and are such that 0 1 0 2 has a unique solution y t the author gives sufficient conditions for the asymptotic stability of the equation 0 1 for which he introduces new definitions of numerical stability the approach is reminiscent of that from the nonlinear stiff ordinary differential equation ode field he investigates stability properties of the class of one point collocation rules in particular the backward euler method turns out to be stable with respect to all the given definitions

group inverses of certain positive operators abstract positive operators on certain polyhedral cones with the property that the group inverse of the operator is equal to some power of the operator are characterized the special case of the moore penrose inverse is also considered

nonequiprobable signaling on the gaussian channel signaling schemes for the gaussian channel based on finite dimensional lattices are considered the signal constellation consists of all lattice points within a region r and the shape of this region determines the average signal power spherical signal constellations minimize average signal power and in the limit as n to infinity the shape gain of the n sphere over the n cube approaches pi e 6 approximately 1 53 db a nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension a signal constellation omega is partitioned into t subconstellations omega sub 0 omega sub tau 1 of equal size by scaling a basic region r signal points in the same subconstellation are used equiprobably and a shaping code selects the subconstellation omega sub i with frequency f sub i shaping codes make it possible to achieve any desired fractional bit rate the schemes presented are compared with equiprobable signaling schemes based on voronoi regions of multidimensional lattices for comparable shape gain and constellation expansion ratio the peak to average power ratio of the schemes presented is superior furthermore a simple table lookup is all that is required to address points in the constellations it is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework

sixth order compact scheme combined with multigrid method and extrapolation technique for 2d poisson equation we develop a sixth order finite difference discretization strategy to solve the two dimensional poisson equation which is based on the fourth order compact discretization multigrid method richardson extrapolation technique and an operator based interpolation scheme we use multigrid v cycle procedure to build our multiscale multigrid algorithm which is similar to the full multigrid method fmg the multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid a sixth order accurate coarse grid solution is computed by using the richardson extrapolation technique then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method compared to sun zhang s sixth order richardson extrapolation compact rec discretization strategy using alternating direction implicit adi method and the standard fourth order compact difference foc scheme using a multigrid method

iterative operator splitting methods with higher order time integration methods and applications for parabolic partial differential equations in this paper we design higher order time integrators for systems of stiff ordinary differential equations we combine implicit runge kutta and bdf methods with iterative operator splitting methods to obtain higher order methods the idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently we compare our new methods with the higher order fractional stepping runge kutta methods developed for stiff ordinary differential equations the benefit is the individual handling of each operator with adapted standard higher order time integrators the methods are applied to equations for convection diffusion reactions and we obtain higher order results finally we discuss the applications of the iterative operator splitting methods to multi dimensional and multi physical problems

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

dmlpg method for specifying a control function in two dimensional parabolic inverse pdes abstract this article describes a fast meshless technique the direct meshless local petrov galerkin dmlpg method for identifying a control function in two dimensional parabolic inverse pdes the dmlpg method is a truly meshless technique that directly approximates the local weak forms in dmlpg the local integrations are done over the low degree polynomial basis functions instead of the complicated shape functions thus the mass and stiff matrices are constructed by integration against polynomials this feature overcomes the main drawback of meshless methods in comparison with the finite element methods fem and significantly increases the computational efficiency in comparison with the other meshless weak form methods in this paper we apply the dmlpg and mlpg methods for solving two dimensional parabolic inverse pdes on regular and irregular domains these methods are compared with each other and the superiority of the dmlpg over the classical mlpg is demonstrated the numerical results confirm the good efficiency of the dmlpg method for solving inverse problems especially coefficient inverse problems finally we will conclude that the dmlpg method can be considered as an attractive alternative to existing meshless weak form methods in solving inverse problems

a geometric treatment of generalized inverses and semigroups of nonnegative matrices abstract the purpose of this paper is to provide a unified treatment from the geometric viewpoint of the following closely related aspects of nonnegative matrices nonnegative matrices with nonnegative generalized inverses of various kinds nonnegative rank factorization regular elements green s relations and maximal subgroups of the semigroups of nonnegative matrices stochastic matrices column stochastic matrices and doubly stochastic matrices

reliable channel regions for good binary codes transmitted over parallel channels we study the average error probability performance of binary linear code ensembles when each codeword is divided into j subcodewords with each being transmitted over one of j parallel channels this model is widely accepted for a number of important practical channels and signaling schemes including block fading channels incremental redundancy retransmission schemes and multicarrier communication techniques for frequency selective channels our focus is on ensembles of good codes whose performance in a single channel model is characterized by a threshold behavior e g turbo and low density parity check ldpc codes for a given good code ensemble we investigate reliable channel regions which ensure reliable communications over parallel channels under maximum likelihood ml decoding to construct reliable regions we study a modifed 1961 gallager bound for parallel channels by allowing codeword bits to be randomly assigned to each component channel the average parallel channel gallager bound is simplified to be a function of code weight enumerators and channel assignment rates special cases of this bound average union bhattacharyya ub shulman feder sf simplified sphere ss and modified shulman feder msf parallel channel bounds allow for describing reliable channel regions using simple functions of channel and code spectrum parameters parameters describing the channel are the average parallel channel bhattacharyya noise parameter the average channel mutual information and parallel gaussian channel signal to noise ratios snrs code parameters include the union bhattacharyya noise threshold and the weight spectrum distance to the random binary code ensemble reliable channel regions of repeat accumulate ra codes for parallel binary erasure channels becs and of turbo codes for parallel additive white gaussian noise awgn channels are numerically computed and compared with simulation results based on iterative decoding in addition an examp

canonical euler splitting method for nonlinear composite stiff evolution equations in this paper a new splitting method called canonical euler splitting method ces is constructed and studied which can be used for the efficient numerical solution of general nonlinear composite stiff problems in evolution equations of various type such as ordinary differential equations odes semi discrete unsteady partial differential equations pdes and ordinary or partial volterra functional differential equations vfdes and can significantly improve the computing speed on the basis of ensuring the computing quality stability consistency and convergence theories of this method are established a series of numerical experiments are given which check the efficiency of ces method and confirm our theoretical results

discretized stability and error growth of the nonautonomous pantograph equation this paper is concerned with the stability properties of runge kutta methods for the pantograph equation a functional differential equation with a proportional delay the focus is on nonautonomous equations both linear and nonlinear cases are considered sufficient and necessary conditions for the asymptotic stability of the numerical solution of general neutral pantograph equations are given an upper bound for the error growth is investigated for algebraically stable methods applied to nonneutral equations finally some stability results are extended to the case of a more general class of equations

a higher order compact lod method and its extrapolations for nonhomogeneous parabolic differential equations abstract a higher order compact locally one dimensional lod finite difference method for two dimensional nonhomogeneous parabolic differential equations is proposed the resulting scheme consists of two one dimensional tridiagonal systems and all computations are implemented completely in one spatial direction as for one dimensional problems the solvability and the stability of the scheme are proved almost unconditionally the error estimates are obtained in the discrete h 1 l 2 and l norms and show that the proposed compact lod method has the accuracy of the second order in time and the fourth order in space two richardson extrapolation algorithms are presented to increase the accuracy to the fourth order and the sixth order in both time and space when the time step is proportional to the spatial mesh size numerical results demonstrate the accuracy of the compact lod method and the high efficiency of its extrapolation algorithms

coded modulation in the block fading channel coding theorems and code construction we consider coded modulation schemes for the block fading channel in the setting where a codeword spans a finite number n of fading degrees of freedom we show that coded modulations of rate r bit per complex dimension over a finite signal set spl chi spl sube spl copf of size 2 sup m achieve the optimal rate diversity tradeoff given by the singleton bound spl delta n m r 1 spl lfloor n 1 r m spl rfloor for r spl isin 0 m spl rfloor furthermore we show also that the popular bit interleaved coded modulation achieves the same optimal rate diversity tradeoff we present a novel coded modulation construction based on blockwise concatenation that systematically yields singleton bound achieving turbo like codes defined over an arbitrary signal set spl chi spl sub spl copf the proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block fading channel we analyze the ensemble average performance under maximum likelihood ml decoding of the proposed codes by means of upper bounds and tight approximations we show that differently from the additive white gaussian noise awgn and fully interleaved fading cases belief propagation iterative decoding performs very close to ml on the block fading channel for any signal to noise ratio snr and even for relatively short block lengths we also show that at constant decoding complexity per information bit the proposed codes perform close to the information outage probability for any block length while standard block codes e g obtained by trellis termination of convolutional codes have a gap from outage that increases with the block length this is a different and more subtle manifestation of the so called interleaving gain of turbo codes

some recent developments of numerov s method abstract this paper is a survey of some recent developments of numerov s method for solving nonlinear two point boundary value problems the survey consists of three different parts the existence uniqueness of a solution computational algorithm for computing a solution and some extensions of numerov s method the sufficient conditions for the existence and uniqueness of a solution are presented some of them are best possible various iterative methods are reviewed including picard s iterative method modified newton s iterative method monotone iterative method and accelerated monotone iterative method in particular two more direct monotone iterative methods are presented to save computational work each of these iterative methods not only gives a computational algorithm for computing a solution but also leads to an existence and uniqueness theorem the estimate on the rate of convergence of the iterative sequence is given the extensions of numerov s method to a coupled problem and a general problem are addressed the numerical results are presented to validate the theoretical analysis

higher order compact finite difference method for systems of reaction diffusion equations this paper is concerned with a compact finite difference method for solving systems of two dimensional reaction diffusion equations this method has the accuracy of fourth order in both space and time the existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term three monotone iterative algorithms are provided for solving the resulting discrete system efficiently and the sequences of iterations converge monotonically to a unique solution of the system a theoretical comparison result for the various monotone sequences is given the convergence of the finite difference solution to the continuous solution is proved and richardson extrapolation is used to achieve fourth order accuracy in time an application is given to an enzyme substrate reaction diffusion problem and some numerical results are presented to demonstrate the high efficiency and advantages of this new approach

on the stability and convergence of a difference scheme for an one dimensional parabolic inverse problem abstract the parabolic equation with the control parameter is a class of parabolic inverse problems and is nonlinear while determining the solution of the problems we shall determinate some unknown control parameter these problems play a very important role in many branches of science and engineering this article is devoted to the following parabolic initial and boundary problem with the control parameter u t 2u x2 p t u x t 0

high order contractive runge kutta methods for volterra functional differential equations a contractivity theory of runge kutta methods for stiff nonlinear volterra functional differential equations vfdes is established by means of which a family of high order contractive runge kutta methods for vfdes are identified the application of the general theory for stiff nonlinear vfdes to the special cases of stiff nonlinear delay differential equations and delay integro differential equations is also presented

polynomial chaos for random fractional order differential equations fractional order models provide a powerful instrument for description of memory and hereditary properties of systems in comparison to integer order models where such effects are difficult to incorporate and often neglected also many physical real world problems that involve uncertainties and errors can be best modeled with random differential equations thus to be able to deal with many real life problems it is important to develop mathematical methodologies to solve systems that include both memory effects and uncertainty the aim of this paper is to study the application of the generalized polynomial chaos gpc to random fractional ordinary differential equations the method of polynomial chaos has played an increasingly important role when dealing with uncertainties the main idea of the method is the projection of the random parameters and stochastic processes in the system onto the space of polynomial chaoses however to apply polynomial chaos to random fractional differential equations requires careful attention due to memory effects and the increasing of the computation time in respect to the classic random differential equations in order to avoid more complex numerical computations and obtain accurate solutions we rely on richardson extrapolation it is shown that the application of generalized polynomial chaos method in conjunction with richardson extrapolation is a reliable and accurate method to numerically solve random fractional ordinary differential equations

on the numerical solution of multi dimensional parabolic problem by the additive splitting up method several numerical methods arising from the difference methods for certain classes of two dimensional parabolic equation are based on an operator slitting from the theoretical point of view the success and the evaluation of the splitting approach is primarily determined by the accuracy and the stability constrained most of the splitting methods defined in the past decades were of multiplicative non parallel types with respect to the spatial variables in 1994 lui tai and neittaanmaki presented a parallelisable implicit splitting type of methods of different order of approximation and its of additive type with regard to the solution at the advanced time step in this paper the stability analysis will be presented for the implicit splitting methods by lu et al and also we presented a parallelisable explicit splitting algorithm several model problems are solved by the splitting up algorithms to enhance the theoretical results and the concluding remarks

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

a fourth order compact adi method for solving two dimensional unsteady convection diffusion problems n this article an exponential high order compact ehoc alternating direction implicit adi method in which the crank nicolson scheme is used for the time discretization and an exponential fourth order compact difference formula for the steady state 1d convection diffusion problem is used for the spatial discretization is presented for the solution of the unsteady 2d convection diffusion problems the method is temporally second order accurate and spatially fourth order accurate which requires only a regular five point 2d stencil similar to that in the standard second order methods the resulting ehoc adi scheme in each adi solution step corresponds to a strictly diagonally dominant tridiagonal matrix equation which can be inverted by simple tridiagonal gaussian decomposition and may also be solved by application of the one dimensional tridiagonal thomas algorithm with a considerable saving in computing time the unconditionally stable character of the method was verified by means of the discrete fourier or von neumann analysis numerical examples are given to demonstrate the performance of the method proposed and to compare mostly it with the high order adi method of karaa and zhang and the spatial third order compact scheme of note and tan

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

general linear methods for volterra integro differential equations with memory a new class of numerical methods for volterra integro differential equations with memory is developed the methods are based on the combination of general linear methods with compound quadrature rules sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established numerical examples illustrate the convergence and effectiveness of the numerical methods

high accuracy difference schemes for the system of two space nonlinear parabolic differential equations with mixed derivatives and variable coefficients abstract in this article two level compact implicit difference methods of o k2 kh2 h4 using 9 spatial grid points are proposed for the numerical solution of the system of two dimensional nonlinear parabolic equations with variable coefficients subject to the dirichlet boundary conditions where k 0 and h 0 are step lengths in time and space directions respectively the proposed difference method for scalar equation is applied for the solution of the heat conduction equation in polar coordinates to obtain the two level unconditionally stable adi method of o k2 h4 the method having two variables also has been successfully applied on two dimensional unsteady navier stokes model equations in polar coordinates some numerical examples are presented to demonstrate the accuracy of the implementation

error estimate of fourth order compact scheme for linear schrodinger equations a fourth order compact difference scheme is proposed for two dimensional linear schrodinger equations with periodic boundary conditions by using the discrete energy method it is proven that the difference scheme is uniquely solvable unconditionally stable and convergent a maximum norm error estimate and thus an asymptotic expansion of the discrete solution are also obtained using the expansion of the difference solution high order approximations could be achieved by richardson extrapolations extension to three dimensional problems is also discussed numerical experiments are included to support the theoretical results and comparisons with the crank nicolson method are presented to show the effectiveness of our method

an analysis of the block error probability performance of iterative decoding asymptotic iterative decoding performance is analyzed for several classes of iteratively decodable codes when the block length of the codes n and the number of iterations i go to infinity three classes of codes are considered these are gallager s regular low density parity check ldpc codes tanner s generalized ldpc gldpc codes and the turbo codes due to berrou et al it is proved that there exist codes in these classes and iterative decoding algorithms for these codes for which not only the bit error probability p sub b but also the block frame error probability p sub b goes to zero as n and i go to infinity

a new adi technique for two dimensional parabolic equation with an integral condition abstract nonclassical parabolic initial boundary value problems arise in the study of several important physical phenomena this paper presents a new approach to treat complicated boundary conditions appearing in the parabolic partial differential equations with nonclassical boundary conditions a new fourth order finite difference technique based upon the noye and hayman n h alternating direction implicit adi scheme is used as the basis to solve the two dimensional time dependent diffusion equation with an integral condition replacing one boundary condition this scheme uses less central processor time cpu than a second order fully implicit scheme based on the classical backward time centered space btcs method for two dimensional diffusion it also has a larger range of stability than a second order fully explicit scheme based on the classical forward time centered space ftcs method the basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyeet this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference methods the results of numerical experiments for the new method are presented the central processor times needed are also reported error estimates derived in the maximum norm are tabulated

precoding by pairing subchannels to increase mimo capacity with discrete input alphabets we consider gaussian multiple input multiple output mimo channels with discrete input alphabets we propose a non diagonal precoder based on the x codes in to increase the mutual information the mimo channel is transformed into a set of parallel subchannels using singular value decomposition svd and x codes are then used to pair the subchannels x codes are fully characterized by the pairings and a 2 2 real rotation matrix for each pair parameterized with a single angle this precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs the problem of finding the optimal precoder with the above structure which maximizes the total mutual information is solved by i optimizing the rotation angle and the power allocation within each pair and ii finding the optimal pairing and power allocation among the pairs it is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal pre coder by cruz et al and is significantly better than mercury waterfllling strategy by lozano et al our approach greatly simplifies both the precoder optimization and the detection complexity making it suitable for practical applications

multigrid method and fourth order compact scheme for 2d poisson equation with unequal mesh size discretization abstract a fourth order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two dimensional poisson equation in a rectangular domain multigrid methods using a partial semicoarsening strategy and line gauss seidel relaxation are designed to solve the resulting sparse linear systems numerical experiments are conducted to test the accuracy of the fourth order compact difference scheme and to compare it with the standard second order difference scheme convergence behavior of the partial semicoarsening and line gauss seidel relaxation multigrid methods is examined experimentally

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

short note a high order pade adi method for unsteady convection diffusion equations a high order alternating direction implicit adi method for computations of unsteady convection diffusion equations is proposed by using fourth order pade schemes for spatial derivatives the present scheme is fourth order accurate in space and second order accurate in time the solution procedure consists of a number of tridiagonal matrix operations which make the computation cost effective the method is unconditionally stable and shows higher accuracy and better phase and amplitude error characteristics than the standard second order adi method d w peaceman h h rachford jr the numerical solution of parabolic and elliptic differential equations journal of the society of industrial and applied mathematics 3 1959 28 41 and the fourth order adi scheme of karaa and zhang high order adi method for solving unsteady convection diffusion problem journal of computational physics 198 2004 1 9

generalized inverses of cone preserving maps abstract let k 1 and k 2 be solid cones in r n and r m respectively and let a be a linear operator such that ak 1 k 2 necessary and sufficient conditions for the existence of various kinds of generalized inverses of a taking k 2 into k 1 are given projections which belong to k the set of all linear operators that preserve a are studied in particular it is proved that a projection p in k is a simplicial nonnegative linear combination of its rank one operators iff im p k is a simplical cone an open question of burns fiedler and haynsworth concerning minimal generating matrices of polyhedral cones is also extended and answered affirmatively

a compact lod method and its extrapolation for two dimensional modified anomalous fractional sub diffusion equations a crank nicolson type compact locally one dimensional lod finite difference method is proposed for a class of two dimensional modified anomalous fractional sub diffusion equations with two time riemann liouville fractional derivatives of orders 1 and 1 0 1 the resulting scheme consists of simple tridiagonal systems and all computations are carried out completely in one spatial direction as for one dimensional problems this property evidently enhances the simplicity of programming and makes the computations more easy the unconditional stability and convergence of the scheme are rigorously proved the error estimates in the standard h 1 and l 2 norms and the weighted l norm are obtained and show that the proposed compact lod method has the accuracy of the order 2 min in time and 4 in space a richardson extrapolation algorithm is presented to increase the temporal accuracy to the order min 4 min if and min 1 4 if a comparison study of the compact lod method with the other existing methods is given to show its superiority numerical results confirm our theoretical analysis and demonstrate the accuracy and the effectiveness of the compact lod method and the extrapolation algorithm

extrapolation algorithm of compact adi approximation for two dimensional parabolic equation abstract in this paper we propose a compact alternating direction implicit adi scheme for solving the two dimensional parabolic equation the maximum norm convergence is proven and the convergence rate is second order in time and fourth order in space we develop a richardson extrapolation algorithm to increase the accuracy to sixth order both in time and space numerical experiments show the effectiveness of the method

high order compact adi methods for parabolic equations in this paper we develop a sixth order compact scheme coupled with alternating direction implicit adi methods and apply it to parabolic equations in both 2 d and 3 d unconditional stability is proved for linear diffusion problems with periodic boundary conditions numerical examples supporting our theoretical analysis are provided

analysis of operator splitting for advection diffusion reaction problems from air pollution modelling abstract operator or time splitting is often used in the numerical solution of initial boundary value problems for differential equations it is for example standard practice in computational air pollution modelling where we encounter systems of three dimensional time dependent partial differential equations of the advection diffusion reaction type for such systems little attention has been devoted to the analysis of splitting and to the question why splitting can work so well from the theoretical point of view the success of splitting is primarily determined by the splitting error this paper presents an analysis of operator splitting aimed at providing insight into the splitting error using the lie operator formalism a general expression is derived for a three term strang splitting in the pure initial value case for a class of advection diffusion reaction problems the splitting error is analyzed in greater detail a special case is discussed in which the splitting error can be reduced also some attention is paid to the use of operator splitting in initial boundary value problems

stability analysis of volterra delay integro differential equations and their backward differentiation time discretization we study the stability of the analytical solutions of initial value problems of a general class of systems of volterra delay integro differential equations numerical methods based on backward differentiation formulae and repeated quadrature formulae are suggested nonlinear and linear stability conditions for the presented methods are derived

a comparative study of adi splitting methods for parabolic equations in two space dimensions abstract the main purpose of the paper is a numerical comparison of three integration methods for semi discrete parabolic partial differential equations in two space variables linear as well as nonlinear equations are considered the integration methods are the well known adi method of peaceman and rachford a global extrapolation scheme of the classical adi method to order four and a fourth order four step adi splitting method

low density parity check codes for nonergodic block fading channels we design powerful low density parity check ldpc codes with iterative decoding for the block fading channel we first study the case of maximum likelihood decoding and show that the design criterion is rather straightforward since optimal constructions for maximum likelihood decoding do not perform well under iterative decoding we introduce a new family of full diversity ldpc codes that exhibit near outage limit performance under iterative decoding for all block lengths this family competes favorably with multiplexed parallel turbo codes for nonergodic channels

classical theory of runge kutta methods for volterra functional differential equations abstract for solving volterra functional differential equations vfdes a class of discrete runge kutta methods based on canonical interpolation is studied which was first presented by the same author in a previous published paper classical stability and convergence theories for this class of methods are established the methods studied and the theories established in this paper can be directly applied to non stiff non linear initial value problems in delay differential equations ddes integro differential equations ides delay integro differential equations dides and vfdes of other type which appear in practice and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff vfdes

outage probability of the free space optical channel with doubly stochastic scintillation we study the asymptotic outage probability of multiple input multiple output free space optical communication with pulse position modulation in particular we consider doubly stochastic scintillation models lognormal rice and i k distributions first we consider the case when channel state information is available at the receiver only then we consider the case when it is also available at the transmitter

adams methods for neutral functional differential equations in this paper adams type methods for the special case of neutral functional differential equations are examined it is shown thatk step methods maintain orderk 1 for sufficiently small step size in a sufficiently smooth situation however when these methods are applied to an equation with a non smooth solution the order of convergence is only one some computational considerations are given and numerical experiments are presented

stability of runge kutta methods for the generalized pantograph equation this paper deals with stability properties of runge kutta rk methods applied to a non autonomous delay differential equation dde with a constant delay which is obtained from the so called generalized pantograph equation an autonomous dde with a variable delay by a change of the independent variable it is shown that in the case where the rk matrix is regular stability properties of the rk method for the dde are derived from those for a difference equation which are examined by similar techniques to those in the case of autonomous ddes with a constant delay as a result it is shown that some rk methods based on classical quadrature have a superior stability property with respect to the generalized pantograph equation stability of algebraically stable natural rk methods is also considered

optimum power allocation for parallel gaussian channels with arbitrary input distributions the mutual information of independent parallel gaussian noise channels is maximized under an average power constraint by independent gaussian inputs whose power is allocated according to the waterfilling policy in practice discrete signaling constellations with limited peak to average ratios m psk m qam etc are used in lieu of the ideal gaussian signals this paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions such policy admits a graphical interpretation referred to as mercury waterfilling which generalizes the waterfilling solution and allows retaining some of its intuition the relationship between mutual information of gaussian channels and nonlinear minimum mean square error mmse proves key to solving the power allocation problem

b convergence theory of runge kutta methods for stiff volterra functional differential equations with infinite integration interval in this paper b convergence theory of runge kutta methods for nonlinear stiff volterra functional differential equations is extended from finite integration interval a t to infinite integration interval a infty the results obtained are of importance for the study of functional differential dynamic systems and for long time stiff computation

a two level linearized compact adi scheme for two dimensional nonlinear reaction diffusion equations abstract a novel two level linearized compact alternating direction implicit adi scheme is proposed for solving two dimensional nonlinear reaction diffusion equations the computational cost is reduced by use of the newton linearized method and the adi method the existence and uniqueness of the numerical solutions are proved moreover the error estimates in h 1 and l norms are presented numerical examples are given to illustrate our theoretical results

a perspective on the numerical treatment of volterra equations abstract we discuss the properties and numerical treatment of various types of volterra and abel volterra integral and integro differential equations

an accurate lod scheme for two dimensional parabolic problems we propose a high order locally one dimensional scheme for solving parabolic problems the method is fourth order in space and second order in time and provides a computationally efficient implicit scheme it is shown through a discrete fourier analysis that the method is unconditionally stable numerical experiments are conducted to test its high accuracy and to compare it with other schemes

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

numerical analysis of coupled systems of nonlinear parabolic equations this paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method three monotone iteration processes for the finite difference system are presented and the sequences of iterations are shown to converge monotonically to a unique solution of the system including an existence uniqueness comparison theorem a theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary value problem an application to a reaction diffusion model in chemical engineering and combustion theory is given

stability of runge kutta methods for delay integro differential equations we study stability of runge kutta rk methods for delay integro differential equations with a constant delay on the basis of the linear equation du dt lu t mu t k t t u d where l m k are constant complex matrices in particular we show that the same result as in the case k 0 koto bit 34 1994 262 267 holds for this test equation i e every a stable rk method preserves the delay independent stability of the exact solution whenever a step size of the form h m is used where m is a positive integer

locally explicit schemes for three dimensional diffusion with a non local boundary specification two finite difference schemes based on the classical three point forward time centred space ftcs method and the five point ftcs formula are used to solve the three dimensional time dependent diffusion equation with a non local boundary specification in these methods locally one dimensional lod procedures are used to extend the one dimensional techniques to solve the three dimensional problem numerical integration procedures are also employed to overcome the non local boundary specification results from some numerical experiments are presented including error estimates derived in the maximum norm the results of numerical testing show that the lod techniques give better results than the fully explicit schemes the cpu times used for the procedures developed in this article are also reported