exponentially fitted spline in compression for the numerical solution of singular perturbation problems abstract some exponentially fitted difference schemes for singularly perturbed two point boundary value problems are derived using spline in compression these schemes are second order accurate numerical examples are given in support of the theoretical results

performance of optimum and suboptimum combining diversity reception for binary and quadrature dpsk over independent nonidentical rayleigh fading channels this paper is concerned with the error performance analysis of binary and quadrature differential phase shift keying with differential detection over the nonselective rayleigh fading channel with combining diversity reception the diversity channels are independent but have nonidentical statistics the fading process in each channel is assumed to have an arbitrary doppler spectrum with arbitrary doppler bandwidth both optimum diversity reception and suboptimum diversity reception are considered results available previously apply only to the case of second order diversity and require numerical integration for their actual evaluation our results are more general in that the order of diversity is arbitrary moreover the bit error probability bep result is obtained in an exact closed form expression which shows the behavior of the bep as an explicit function of the one symbol interval fading correlation coefficient at the matched filter output the mean received signal to noise ratio per symbol per channel and the order of diversity

high order finite difference techniques for linear singular perturbation boundary value problems abstract three high order finite difference techniques are developed for the second order singularity perturbed linear boundary value problem in one dimension taylor series expansions and error conversions are used for the development of the techniques convergence and stability conditions of these techniques are proved and some numerical results are given

bit error probabilities of 2 and 4dpsk with nonselective rayleigh fading diversity reception and correlated gaussian interference a new analytical approach is presented for deriving the bit error probability results for 2 and 4dpsk with differential detection over the nonselective rayleigh fading channel with diversity reception and with an additional additive correlated gaussian interference process in each diversity channel the approach differs from that in a previous paper and is based on a well known result in the literature the results are new and reduce to known results when the correlated interference is absent they show that the correlated interference behaves like an additional component of the information bearing signal and affects the error probabilities of the various transmitted symbols differently irrespective of its statistical distribution its gaussian statistical distribution is essential only for the analysis of the bit error probability

least squares spectral collocation for discontinuous and singular perturbation problems a least squares spectral collocation scheme for discontinuous problems is proposed for the first derivative operator the domain is decomposed in subintervals where the jumps are imposed at the discontinuities equal order polynomials are used on all subdomains for the discretization spectral collocation with chebyshev polynomials is employed fast fourier transforms are now available the collocation conditions and the interface conditions lead to an overdetermined system which can be efficiently solved by least squares the solution technique will only involve symmetric positive definite linear systems this approach is further extended to singular perturbation problems where least squares are used for stabilization by a suitable decomposition of the domain the boundary layer is well resolved numerical simulations confirm the high accuracy of our spectral least squares scheme

solving singularly perturbed problems by a weak form integral equation with exponential trial functions abstract the second order singularly perturbed problem is transformed to a singularly perturbed parabolic type partial differential equation by using a fictitious time technique then we use green s second identity to derive a boundary integral equation in terms of the adjoint trefftz test functions namely a weak form integral equation method wfiem it accompanying with the exponential trial functions which are designed to satisfy the boundary conditions automatically can provide very accurate numerical solutions of linear and nonlinear singularly perturbed problems for the latter problem the iterative procedure is convergent very fast

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

on the numerical solution of differential algebraic equations by pade series in this paper the solution for a differential algebraic equation dae can be expanded up to arbitrary order using maple computer algebra systems frank maple v crc press boca raton fl 1996 first we calculate power series of the given equations system then transform it into pade series form which gives an arbitrary order for solving dae numerically

a mechanical algorithm for solving ordinary differential equation in this paper by using the theories and methods of mathematics analysis ordinary differential equation and computer algebra a reliable algorithm for solving ordinary differential equation ode was established and a new maple procedure mechodeproc was established too the results of the examples indicated that the procedure mechodeproc based on taylor polynomial method was simple and effective and could provide an accuracy approximate solution or exact solution of the ordinary differential equation this would be useful for solving differential equation

numerical patching method for singularly perturbed two point boundary value problems using cubic splines a numerical patching method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end left or right point the method is distinguished by the following fact the original singularly perturbed two point boundary value problem is divided into two problems namely inner and outer region problems the terminal boundary condition is obtained from the solution of the reduced problem using general stretching transformation a modified inner region problem is constructed then both inner region problem and outer region problems are solved as two point boundary value problems by employing cubic splines several linear and non linear problems are solved to demonstrate the applicability of the method

a direct solver for the least squares spectral collocation system on rectangular elements for the incompressible navier stokes equations a least squares spectral collocation scheme for the stokes and incompressible navier stokes equations is proposed the original domain is decomposed into quadrilateral subelements and on the element interfaces continuity of the functions is enforced in the least squares sense the collocation conditions and the interface conditions lead to overdetermined systems these systems are directly solved by qr decomposition of the underlying matrices by numerical simulations it is shown that the direct method leads to better results than the approach with normal equations furthermore it is shown that the condition numbers can be reduced by introducing the clenshaw curtis quadrature rule for imposing the average pressure to be zero finally our scheme is successfully applied to the regularized and lid driven cavity flow problems

a study on a boundary layer equation arising in an incompressible fluid in this paper a differential equation of mixing layer that arises in viscous incompressible fluid will be investigated the series solution method will be effectively implemented to a related integro differential equation the condition at infinity will be applied to a related pade approximants of the obtained series solution

a new algorithm for symbolic integral with application in this paper by using the theories and methods of mathematical analysis and computer algebra a new algorithm of symbolic integral was established a new maple procedure myint for it was established too and it was applied to the automatic proving the mean value theorems for derivatives the results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea excellent property for operation and powerful competence this would be useful for the problem of solving differential equations automatic proving some mathematical theorems and so on

mass and momentum conservation of the least squares spectral collocation method for the navier stokes equations from the literature it is known that the least squares spectral element method lssem for the stationary stokes equations performs poorly with respect to mass conservation but compensates this lack by a superior conservation of momentum furthermore it is known that the least squares spectral collocation method lsscm leads to superior conservation of mass and momentum for the stationary stokes equations in the present paper we consider mass and momentum conservation of the lsscm for time dependent stokes and navier stokes equations we observe that the lsscm leads to improved conservation of mass and momentum for these problems furthermore the lsscm leads to the well known time dependent profiles for the velocity and the pressure profiles to obtain these results we use only a few elements each with high polynomial degree avoid normal equations for solving the overdetermined linear systems of equations and introduce the clenshaw curtis quadrature rule for imposing the average pressure to be zero furthermore we combined the transformation of gordon and hall transfinite mapping with the least squares spectral collocation scheme to discretize the internal flow problems

computing the eigenvalues of the generalized sturm liouville problems based on the lie group sl 2 r for the generalized sturm liouville problems we can construct an sl 2 r lie group shooting method to find eigenvalues by using the closure property of the lie group a one step lie group transformation between the boundary values at two ends of the considered interval is established hence we can theoretically derive an analytical characteristic equation to determine the eigenvalues for the generalized sturm liouville problems because the closed form formulas are derived to calculate the unknown left boundary values in terms of l the present method provides an easy numerical implementation and has a cheap computational cost numerical examples are examined to show that the present sl 2 r lie group shooting method is effective

least squares finite element formulations for viscous incompressible and compressible fluid flows abstract we present least squares based finite element formulations for the numerical solution of viscous fluid flows governed by the navier stokes equations as an alternate approach to the well known weak form galerkin finite element formulations the use of least squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise and the resulting linear algebraic problem will have a symmetric positive definite coefficient matrix we address the issue of norm equivalence of the least squares functional and its implications on the resulting finite element model in particular we develop an understanding of the compromise that must exist between the optimality and practicality of the finite element model the latter measured in terms of c k regularity across inter element boundaries we show through numerical examples that for the traditional c 0 basis such a compromise is possible when high p levels are used to span the finite element spaces when a low p level solution is desired guidelines are presented to obtain a reliable least squares collocation solution numerical examples are presented to demonstrate the high and low p level approaches these include incompressible flow past two circular cylinders in a side by side arrangement for gap sizes s d 2 0 and 0 85 incompressible flow past a square cylinder and subsonic transonic and supersonic compressible flow past a circular cylinder in addition we present a discontinuous least squares formulation where c k regularity across inter element boundaries is enforced in a weak sense through the least squares functional allowing for h and p type non conformities in the computational domain

numerical solution of differential algebraic equation systems and applications in this paper the method is developed to differential algebraic equations systems more effective method is presented and illustrated by numerical example the solution for a differential algebraic equation can be expanded up to arbitrary order using maple computer algebra systems first we calculate power series of the given equations system then transform it into pade series form which give an arbitrary order for solving differential algebraic equation numerically

a computational method for solving third order singularly perturbed boundary value problems in this paper a new computational method is presented for solving a class of third order singularly perturbed boundary value problems with a boundary layer at the left of the underlying interval in this method first the given third order singularly perturbed boundary value problem is transformed into a system of two odes subject to suitable initial and boundary conditions and a zeroth order asymptotic expansion for the solution of the given problem is constructed then the reduced terminal value problem is solved analytically in the reproducing kernel space this method is effective and easy to implement a numerical examples is studied to demonstrate the accuracy of the present method results obtained by the method are found to be in good agreement with the exact solution not only in the boundary layer but also away from the layer

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

on the numerical solution of chemical differential algebraic equations by pade series in this paper the solution of chemical differential algebraic equation model of general type f y y x 0 has been done using the method the example including a model of an absorption tower is given to illustrate the utility of the method using maple computer algebra systems

an algorithm for solving the high order nonlinear volterra fredholm integro differential equation with mechanization abstract in this paper by using the theories and methods of mathematics analysis and computer algebra a reliable algorithm for solving high order nonlinear volterra fredholm integro differential equations was established and a new maple procedure voltfredproc was established too the results of the examples indicated that the procedure voltfredproc of taylor polynomial method is simple and effective and could provide an accuracy approximate solution or exact solution of the high order nonlinear volterra fredholm integro differential equation this would be useful for solving integro differential equation integral equations and ordinary differential equation

numerical solutions of chemical differential algebraic equations in this paper the solution for a chemical differential algebraic equation dae can be expanded up to arbitrary order using maple computer algebra systems first we calculate power series of the given equations system then transform it into pade series form which give an arbitrary order for solving chemical dae numerically

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

using reproducing kernel for solving a class of singularly perturbed problems this paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of partial differential equations with a singularly perturbed term in a reproducing kernel space two numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

a novel method for a class of nonlinear singular perturbation problems in this paper we present a boundary value method for solving a class of nonlinear singularly perturbed two point boundary value problems with a boundary layer at the left of the underlying interval this method is based on ideas of singular perturbation analysis by constructing a modified problem with a boundary layer correction we deal with the boundary layer separately and use series method the condition at infinity will be applied to the corresponding pade approximates of the obtained series solution

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

on c algebras having linear polynomial and subexponential growth answering a question of voiculescu 16 problem 5 9 we show thatc algebras having filtrations an n satisfying the condition lim supn ln diman n 0 in particular having subexponential growth are nuclear

analytical approximate solutions of systems of fractional algebraic differential equations by homotopy analysis method abstract in this paper we develop a framework to obtain approximate solutions to systems of algebraic differential equations of fractional order by employing the homotopy analysis method ham the study highlights the efficiency of the method and its dependence on the auxiliary parameter numerical examples are examined to highlight the significant features of the ham method the method shows improvements over existing analytical techniques

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

an algorithm for solving nonlinear singular perturbation problems with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving nonlinear singular perturbation problems was established a new maple procedure spp was established too the procedure spp give not only the approximate analytic solutions but also the numerical solutions of spp six examples are presented to illustrate the implementation of the program the method is very simple and effective for most of singular perturbation problems this would be useful for solving differential equations

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

arbitrary order numerical method for solving differential algebraic equation by pade series in this paper the solution for a differential algebraic equation can be expanded up to arbitrary order using maple computer algebra systems maple v crc press boca raton fl 33431 1996 first we calculate power series of the given equations system then transform it into pade series form which give an arbitrary order for solving differential algebraic equation numerically

an exponentially fitted finite difference method for singular perturbation problems in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end left or right point a fitting factor is introduced in a tridiagonal finite difference scheme and is obtained from the theory of singular perturbations thomas algorithm is used to solve the system the stability of the algorithm is investigated several linear and nonlinear problems are solved to demonstrate the applicability of the method it is observed that the present method approximates the exact solution very well

conservation of mass and momentum of the least squares spectral collocation scheme for the stokes problem from the literature it is known that spectral least squares schemes perform poorly with respect to mass conservation and compensate this lack by a superior conservation of momentum this should be revised since the here presented new least squares spectral collocation scheme leads to an outstanding performance with respect to conservation of momentum and mass the reasons can be found in using only a few elements each with high polynomial degree avoiding normal equations for solving the overdetermined linear systems of equations and by introducing the clenshaw curtis quadrature rule for imposing the average pressure to be zero furthermore we combined the transformation of gordon and hall transfinite mapping with our least squares spectral collocation scheme to discretize the internal flow problems

further results on the bit error probabilities of mdpsk over the nonselective rayleigh fading channel with diversity reception this paper presents a fundamental approach for deriving the bit error probability of bdpsk and qdpsk over the nonselective rayleigh fading channel for a receiver with an arbitrary if filter and for a fading process with an arbitrary doppler spectrum with arbitrary doppler bandwidth the results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small doppler bandwidth compared to the symbol rate this allows the error probability to be studied in the presence of varying degrees of isi due to the bandlimitation of the received signal by the if filter and in the presence of fading fluctuations of various rates the analytical approach presented is simple and yet powerful in that it can handle the case of diversity reception this is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval the bit error probability results apply to both conventional bdpsk and qdpsk as well as spl pi 2 2dpsk and spl pi 4 4dpsk and allow the irreducible bit error probability as well as the snr at which this irreducible value sets in to be studied as a function of the doppler bandwidth and if filter bandwidth the computed results are applicable to the design of digital cellular mobile communication systems

a new mechanical algorithm for solving the second kind of fredholm integral equation integral equation has been one of principal tool of various areas of applied mathematics physics and engineering in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of fredholm integral equation is established and a mechanical maple algorithm fredholmproc is established too the algorithm can provide the continuous solution of the second kind of fredholm integral equation ten examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for solving the integral equation

runge kutta methods for daes a new approach abstract given a linear variable coefficient dae the logarithmic norm of a pencil related to the original pencil a t b t allows us to determine the contractivity of a t x t when algebraically stable runge kutta methods are used for daes the contractivity for an 1xn 1 is no longer maintained for all stepsize in this paper we define a new approach for runge kutta methods that preserve contractivity

an algorithm for adomian decomposition method in this paper a reliable technique for calculating adomian polynomials for nonlinear operators is developed the algorithm is fulfilled with symbolic computation so that the adomian decomposition methods for solving differential equations can be mechanized in maple ten examples are presented to illustrate the implementation of the program

free subalgebras of c algebras abstract the aim of this work is to study the existence of free subalgebras in c algebras the kurosh levitzky problem and related conjectures of makar limanov are answered in the context of c algebras in particular we characterize and study the existence of free non abelian subalgebras with two self adjoint contractions in finitely generated c algebras c algebras having linear growth are shown to be subhomogeneous

numerical integration method for general singularly perturbed two point boundary value problems in this paper a numerical integration method is presented for solving general singularly perturbed two point boundary value problems the original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument then the trapezoidal formula is used to obtain the three term recurrence relationship the proposed method is iterative on the deviating argument to demonstrate the applicability of the method we have solved several model linear and non linear examples with left end boundary layer or right end boundary layer or an internal layer or two boundary layers and presented the computational results

numerical methods for singular perturbation problems consider the two point boundary value problem for a stiff system of ordinary differential equations an adaptive method to solve these problems even when turning points are present is discussed

numerical solutions of linear and nonlinear singular perturbation problems a new method is developed by detecting the boundary layer of the solution of a singular perturbation problem on the non boundary layer domain the singular perturbation problem is dominated by the reduced equation which is solved with standard techniques for initial value problems while on the boundary layer domain it is controlled by the singular perturbation its numerical solution is provided with finite difference methods of which up to sixth order methods are developed the numerical error is maintained at the same level with a constant number of mesh points for a family of singular perturbation problems numerical experiments support the analytical results

non standard difference schemes for singular perturbation problems revisited non standard finite difference techniques for solving various linear two point singularly perturbed boundary value problems are considered they consist of replacing the original differential equation by a related differential equation with a small deviating argument this related problem is then discretized using finite differences this discretized problem is solved using standard matrix methods the accuracy and robustness of these numerical schemes are then carefully investigated and compared to standard centered finite differences in particular earlier claims for the superiority of such schemes over standard finite differences are shown to be invalid

dynamical analysis and perturbation solution of an seir epidemic model abstract in this paper we present a kind of technique to obtain the asymptotical solution of an seir where s is the susceptible population e is the exposed population i is the infectious population and r is the recovered population epidemic model by employing the method of perturbation at first we investigate the epidemic model by analysing its dynamical behavior then we use the method of perturbation to obtain the analytical solution of the model we assign values for parameters and draw figures to observe the magnitude of error of the perturbation method in a macro view finally we analyse macroscopically the two comparison chart on analytical solution and the exact solution and know that it is feasible to analyse the solution of the epidemic model by using the perturbation method

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

on the numerical solution of differential algebraic equations with index 2 in this paper numerical solution of differential algebraic equations daes with index 2 is considered an index reduction for dae with index 2 is suggested first index 2 system is reduced to index 1 system then we have applied the method for solving daes with index 2 numerically

a mechanical algorithm for solving the volterra integral equation in this paper by using the theories and methods of integral equation and computer algebra a reliable algorithm for solving the volterra integral equation is established and a new maple algorithm mainproc is established too some examples are presented to illustrate the implementations of the algorithm the results of the examples indicate that the algorithm of taylor polynomial method is simple and effective and can provide an accuracy approximate solution or exact solution of the volterra integral equation and integro differential equation this will be useful for solving a system of integral equation or integro differential equation

mechanization for solving spp by reducing order method in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of reduction of order approximation method for solving singular perturbation problems was established a new maple procedure redordproc was established too the procedure redordproc give not only the approximate analytic solutions but also the numerical solutions of the kinetics problems some examples are presented to illustrate the implementation of the program

an operator compact implicit method of exponential type a fourth order accurate tridiagonal operator compact implicit finite difference method for diffusion convection equations is developed the coefficients of the difference operator contain exponentials of the coefficients of the differential operator in this way the method avoids spurious oscillations when the cell reynolds number is large numerical results and comparisons to other methods are presented

stable high order methods for differential equations with small coefficients for the second order terms abstract stable high order methods are developed for solving differential equations with small coefficients for the second order terms in particular second fourth and sixth order methods are developed the methods are developed for general linear two point boundary value problems and proved to be stable and accurate results are presented for the one dimensional convection diffusion equation involving problems with and without boundary layers the methods converged for all values of parameters attempted and the results compared favorably with other methods the methods developed in this paper are accurate stable easy to use and applicable to other problems

a new algorithm for integral of trigonometric functions with mechanization in this paper by using the theories of mathematical analysis the authors systematically studied the problem of integrating of trigonometric functions utilizing omnipotence expressions tan x2 t a new integral algorithm for the integral of trigonometric functions was established and a new maple program trigint for the calculation mechanizing for the integral of trigonometric functions was established trigint could evaluate not only the integral of trigonometric functions utilizing omnipotence expresssions correctly but also all the other kinds of functions the results indicated that the algorithm established in this paper had advantages of simple idea excellent property for operation and powerful competence this would be useful for some calculating problems of engineering mathematics

a new method of stabilization for singular perturbation problems with spectral methods a stabilized treatment of singular perturbation problems with spectral methods is presented the stabilization is achieved by introducing one additional collocation point the resulting overdetermined system leads to the normal equations which yield a stabilized system numerical results in one and two dimensions are presented which show the improved condition number of the stabilized spectral system

a numerical algorithm for singular perturbation problems exhibiting weak boundary layers abstract a class of singularly perturbed two point boundary value problems bvp for second order ordinary differential equations is considered here to avoid the numerical difficulties in the solution to these problems we divide the domain into two subdomains the first bvp is a layer domain problem and the second bvp is a regular domain problem error estimates are derived for the numerical solution numerical examples are provided in support of the proposed method

a note on bifurcation points for index 1 differential algebraic problems the arclength continuation method is proposed for index 1 daes with singular points in particular the cusp points the tangency points and equilibrium points are investigated the numerical iterative matrix is studied at a singular point the numerical examples are given to illustrate the robustness of the continuation method

mechanical algorithm for solving the second kind of volterra integral equation in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of volterra integral equation is established and a new maple procedure voltproc is established too in particular the algorithm can provide the exact solution of the second kind of volterra integral equation by the methods of neumann series and mathematical induction i e the algorithm also can computing the nth term by finite terms of the iterative kernel some examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for the integral equation solving and mathematical theorems automatic proving

computations of multi resultant with mechanization abstract resultant is a classical algebraic tool for determining whether or not a polynomial systems have a common root without explicitly solving for the roots but the complexity of resultants can be very high in practice in this paper by using the theories and methods of computer algebra two reliable algorithms for computing multi resultant problems dixon resultant and macaulay resultant were established two new maple procedures dixonres and macaulayres were established too some examples are presented to illustrate the implementations of the programs this would be useful for solving a system of polynomial equations

a rational spectral collocation method for third order singularly perturbed problems a new numerical method is developed for solving a class of third order singularly perturbed boundary value problems first of all the given problem is transformed into a system of two ordinary differential equations odes subject to suitable initial and boundary conditions then the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of odes according to the asymptotic analysis the location and width of boundary layer of the given problem which are chosen as parameters in the sinh transformation can be determined ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method

on the least squares method abstract it is shown that the theoretical basis of the general least squares method is the bounded inverse theorem this explains why the least squares finite element method lsfem within one mathematical computational framework without any special treatment can provide numerical solutions for all types of partial differential equations error estimates of lsfem for general and elliptic first order systems of partial differential equations are established as an example the incompressible stokes equations are considered the principal part of the stokes equations in the first order velocity pressure vorticity formulation consists of two div curl systems this knowledge is employed to derive all permissible combinations of non standard boundary conditions for the stokes equations and to show that under these conditions the stokes operator is bounded below in the full h1 sense and hence the corresponding lsfem is optimal the numerical results are also given to support this conclusion

numerical solution of linear differential algebraic equations in appl math comput 140 2003 77 and appl math comput in press a reducing and modified reducing index methods have been proposed for some cases of semi explicit daes differential algebraic equations in this paper these methods are generalized to more cases also numerical implementation of generalized methods will be presented through pseudospectral method with domain decomposition in addition aforementioned methods will be considered by some examples

computer aided solving the high order transition probability matrix of the finite markov chain in this paper by using theories of stochastic process and computer algebra a reliable algorithm for computing the high order transition probability matrix of finite markov chain is established a new mechanical procedure markovproc is established too the procedure markovproc give not only the exact expression of the markov chains but also the limiting probability some examples are presented to illustrate the implementation of the algorithm