on testing isomorphism of permutation networks the problem of constructing equivalence maps between two multistage permutation networks is considered a branch and bound algorithm is given to test whether two such networks are equivalent in polynomial time whenever they are the algorithm also determines a map that conjugates one network onto the other

a second order accurate numerical approximation for the fractional diffusion equation fractional order diffusion equations are generalizations of classical diffusion equations treating super diffusive flow processes in this paper we examine a practical numerical method which is second order accurate in time and in space to solve a class of initial boundary value fractional diffusive equations with variable coefficients on a finite domain an approach based on the classical crank nicholson method combined with spatial extrapolation is used to obtain temporally and spatially second order accurate numerical estimates stability consistency and therefore convergence of the method are examined it is shown that the fractional crank nicholson method based on the shifted grunwald formula is unconditionally stable a numerical example is presented and compared with the exact analytical solution for its order of convergence

numerical methods for the solution of partial differential equations of fractional order anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas to model this transport mechanism fractional order space derivative operators can be used here the numerical properties of partial differential equations of fractional order 1 2 are studied two numerical schemes an explicit and a semi implicit one are used in solving these equations two different discretization methods of the fractional derivative operator have also been used the accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order

a new fractional numerical differentiation formula to approximate the caputo fractional derivative and its applications in the present work first a new fractional numerical differentiation formula called the l1 2 formula to approximate the caputo fractional derivative of order 0 1 is developed it is established by means of the quadratic interpolation approximation using three points t j 2 f t j 2 t j 1 f t j 1 and t j f t j for the integrand f t on each small interval t j 1 t j j 2 while the linear interpolation approximation is applied on the first small interval t 0 t 1 as a result the new formula can be formally viewed as a modification of the classical l1 formula which is obtained by the piecewise linear approximation for f t both the computational efficiency and numerical accuracy of the new formula are superior to that of the l1 formula the coefficients and truncation errors of this formula are discussed in detail two test examples show the numerical accuracy of l1 2 formula second by the new formula two improved finite difference schemes with high order accuracy in time for solving the time fractional sub diffusion equations on a bounded spatial domain and on an unbounded spatial domain are constructed respectively in addition the application of the new formula into solving fractional ordinary differential equations is also presented several numerical examples are computed the comparison with the corresponding results of finite difference methods by the l1 formula demonstrates that the new l1 2 formula is much more effective and more accurate than the l1 formula when solving time fractional differential equations numerically

numerical methods for solving a two dimensional variable order anomalous subdiffusion equation australian research council dp0559807 dp0986766 national natural science foundation of china 10271098 natural science foundation of fujian province 2009j01014

the fractional diffusion equation in one space and in one time dimension a diffusion equation is solved where the first time derivative is replaced by the fractional time derivative 0 1 the solution is given in closed form in terms of fox functions

the weak solution of a functional differential equation in a general banach space abstract the existence of a unique weak lipschitz continuous solution of the abstract functional differential equation u t a t u t g t u t t 0 t fde u t t t r 0 is obtained by a fixed point argument here x is a general banach space a t d a t x x is m accretive t 0 t and g is lipschitz continuous in both variables stability properties of this weak solution are given and a first order hyperbolic pde to which the theory can be applied is considered

galerkin method applied to a parabolic evolution problem with nonlocal boundary conditions abstract the present paper is devoted to the investigation of a model parabolic mixed problem with boundary integral conditions arising in the context of thermoelasticity existence uniqueness and continuous dependence upon data of a weak solution of the latter are proved by means of the galerkin method

on permuting properties of regular rectangular sw banyans this correspondence analyzes the permuting properties of a reconfigurable multicomputer architecture based on a regular rectangular sw banyan interconnection network with arbitrary fan out and an arbitrary number of stages an analytical expression for the total number of distinct permutations performable by a rectangular sw banyan in one pass is derived it is shown how the combinatorial power of a rectangular sw banyan increases with the growth of its fan out it is also shown that a two pass unidirectional rectangular sw banyan network can be made rearrangeable by a proper choice of the feedback connection

cross directional control on paper machines using gram polynomials a control algorithm for cross directional basis weight control based on orthogonal polynomials is presented instead of controlling the cross directional values at each point the parameters of the orthogonal polynomials are controlled taking into account the maximum bending moment of the slice lip and the relative stiffness of the slice with respect to the actuators the gram polynomials have inherent ability to limit bending of the slice lip in a way that conventional control does not the slice lip will have smooth deflection governed by the maximum order of the polynomial which can be lowered if the bending limits are exceeded by modelling the measurements and the actuator positions by polynomials the mapping between the actuators and the sensors which is the key element of the current control systems is effectively eliminated computational requirements are greatly reduced by avoiding inverses of large matrices or the inverses are found for a diagonal matrix the performance of the gram polynomial control method is shown to be superior to conventional control methods especially for badly conditioned matrices

approximate calculation of sums i bounds for the zeros of gram polynomials let n be a positive integer and x j be n equidistant points we propose an algorithmic approach for approximate calculation of sums of the form sum j 1 n f x j the method is based on the gaussian type quadrature formula for sums sum j 1 n f x j approx sum k 1 n b n k f g n k n n ll n where g n k n are the zeros of the so called gram polynomials this allows the calculation of sums with very large number of terms n to be reduced to sums with a much smaller number of summands n the first task in constructing such a formula is to calculate its nodes g n k n in this paper we obtain precise lower and upper bounds for g n k n numerical experiments show that the estimates for the zeros g n k n are very sharp and that the proposed method for calculation of sums is efficient

partial functional differential equation with an integral condition and applications to population dynamics in this work we consider a semilinear functional partial differential equation with an integral condition we apply the method of semidiscretization in time to establish the existence and uniqueness of solutions we also study the continuation of the solution to the maximal interval of existence finally we give examples to demonstrate the applications of our results

wright functions as scale invariant solutions of the diffusion wave equation the time fractional diffusion wave equation is obtained from the classical diffusion or wave equation by replacing the first or second order time derivative by a fractional derivative of order 0 2 using the similarity method and the method of the laplace transform it is shown that the scale invariant solutions of the mixed problem of signalling type for the time fractional diffusion wave equation are given in terms of the wright function in the case 0 1 and in terms of the generalized wright function in the case 1 2 the reduced equation for the scale invariant solutions is given in terms of the caputo type modification of the

finite difference approximations for fractional advection dispersion flow equations fractional advection dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium in this paper we develop practical numerical methods to solve one dimensional fractional advection dispersion equations with variable coefficients on a finite domain the practical application of these results is illustrated by modeling a radial flow problem use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site

solutions to rayleigh love equation with constant coefficients and delay forcing term abstract in this paper we applied the rothe time discretization method for establishing the sufficient conditions for the existence and uniqueness of a strong solution of a rayleigh love equation with constant coefficients and delay forcing term subject to history initial and integral conditions we also provided an example to illustrate the main result

least squares finite element solution of a fractional order two point boundary value problem in this paper a theoretical framework for the least squares finite element approximation of a fractional order differential equation is presented mapping properties for fractional dimensional operators on suitable fractional dimensional spaces are established using these properties existence and uniqueness of the least squares approximation is proven optimal error estimates are proven for piecewise linear trial elements numerical results are included which confirm the theoretical results

a classification of cube connected networks with a simple control scheme the correspondence presents three classes of cube connected networks with individual stage control based on a group theoretic modeling of interconnection networks it is shown that these classes of networks retain nonisomorphic groups of permutations although the permutations realizable by such networks are rather limited in number the simplicity of their control scheme makes them attractive moreover the interconnection power of these networks can be enhanced by simulating the networks which belong to one class by any member of that class

high order local discontinuous galerkin method combined with wsgd approximation for a fractional subdiffusion equation abstract in this paper a high order local discontinuous galerkin ldg method combined with weighted and shifted grunwald difference wsgd approximation is developed and discussed for a caputo time fractional subdiffusion equation the time fractional derivative of order 0 1 is approximated by a third order method based on the idea of wsgd operator while the spatial operator is approximated by the ldg method some useful lemmas are first introduced and proved then the analysis of stability and optimal error estimate o t 3 h k 1 are obtained for the ldg method extensive numerical results using p k k 0 1 2 3 elements are presented to validate our theoretical analysis

nonlocal cauchy problem for analytic resolvent integrodifferential equations in banach spaces abstract in this paper we prove the existence of semi classical and mild solutions of nonlinear integrodifferential equations with nonlocal conditions in banach spaces the results are obtained by using the theory of analytic resolvents and schaefer s fixed point theorem

on a time discretization method for a semilinear heat equation with purely integral conditions in a nonclassical function space abstract in this paper we construct a semidiscrete approximate solution to a semilinear one dimensional heat equation subject to integral boundary conditions by means of the rothe discretization in time method the convergence of the approximation scheme obtained is proved yielding the well posedness of the problem considered

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

on limit relations between some families of bivariate hypergeometric orthogonal polynomials in this paper we deal with limit relations between bivariate hypergeometric polynomials we analyze the limit relation from trinomial distribution to bivariate gaussian distribution obtaining the limit transition from the second order partial difference equation satisfied by bivariate hypergeometric kravchuk polynomials to the second order partial differential equation verified by bivariate hypergeometric hermite polynomials as a consequence the limit relation between both families of orthogonal polynomials is established a similar analysis between bivariate hahn and bivariate appell orthogonal polynomials is also presented

a novel approach of high accuracy analysis of anisotropic bilinear finite element for time fractional diffusion equations with variable coefficient abstract in this paper by using bilinear finite element and l 1 approximation a fully discrete scheme is established for time fractional diffusion equation with variable coefficient on anisotropic meshes unconditionally stable analysis of the proposed scheme are presented in both l 2 norm and h 1 norm moreover convergence superclose and superconvergence results are derived by combining interpolation with projection which is the key technique for the numerical analysis specifically by defining a novel projection operator the error estimate between the projection and the exact solution is obtained on anisotropic meshes furthermore high accuracy analysis on interpolation of bilinear finite element and projection is gained by means of some known results about the interpolation and mean value technique based on the related results about projection and interpolation the optimal error estimate in l 2 norm and superclose of interpolation in h 1 norm are deduced by skillfully dealing with fractional derivative at the same time the global superconvergence is presented by employing interpolation postprocessing operator finally numerical results are provided to demonstrate the validity of the theoretical analysis

galerkin spectral method for the fractional nonlocal thermistor problem we develop and analyse a numerical method for the time fractional nonlocal thermistor problem by rigorous proofs some error estimates in different contexts are derived showing that the combination of the backward differentiation in time and the galerkin spectral method in space leads for an enough smooth solution to an approximation of exponential convergence in space

rothe s method for an integrodifferential equation with integral conditions this work deals with an integrodifferential equation with initial newman and integral conditions the existence and uniqueness of the weak solution in an appropriate sense is proved by the method of rothe

a petrov galerkin spectral element method for fractional elliptic problems abstract we develop a new c 0 continuous petrov galerkin spectral element method for one dimensional fractional elliptic problems of the form 0 d x u x u x f x 1 2 subject to homogeneous boundary conditions we employ the standard modal spectral element basis and the jacobi poly fractonomials as the test functions zayernouri and karniadakis 2013 we formulate a new procedure for assembling the global linear system from elemental local mass and stiffness matrices the petrov galerkin formulation requires performing elemental local construction of mass and stiffness matrices in the standard domain only once moreover we efficiently obtain the non local history stiffness matrices in which the non locality is presented analytically for uniform grids we also investigate two distinct choices of basis test functions i local basis test functions and ii local basis with global test functions we show that the former choice leads to a better conditioned system and accuracy while the latter results in ill conditioned linear systems and therefore that is not an efficient and a proper choice of test function we consider smooth and singular solutions where the singularity can occur at boundary points as well as in the interior domain we also construct two non uniform grids over the whole computational domain in order to capture singular solutions finally we perform a systematic numerical study of non local effects via full and partial history fading in order to further enhance the efficiency of the scheme

an inverse sturm liouville problem with a fractional derivative in this paper we numerically investigate an inverse problem of recovering the potential term in a fractional sturm liouville problem from one spectrum the qualitative behaviors of the eigenvalues and eigenfunctions are discussed and numerical reconstructions of the potential with a newton method from finite spectral data are presented surprisingly it allows very satisfactory reconstructions for both smooth and discontinuous potentials provided that the order a 1 2 of fractional derivative is sufficiently away from 2

the method of lines applied to nonlinear nonlocal functional differential equations this paper discusses nonlinear functional differential equation in a real reflexive banach space with nonlocal history condition by using the method of lines the existence and uniqueness of a strong solution are established finally some applications of the abstract results are presented

routing algorithms for cellular interconnection arrays the paper describes an algebraic model which provides a means for realizing an arbitrary permutation through various cellular array type networks the model views a cellular array as an ordered set of transposition maps where each transposition corresponds to a permutation cell of the array a permutation realizable by such an array is then expressed as a composition of the transpositions where the rules for the composition are determined by the topology of the array

partitioning a graph in o a log2 v abstract we present an o a log 2 v algorithm to partition a graph where v is the set of vertices and a the set of arcs extending hopcroft s fast partitioning algorithm

fourth order compact scheme for space fractional advection diffusion reaction equations with variable coefficients abstract in this work a new fourth order compact approximation is derived for riemann liouville space fractional derivatives modified wave numbers are obtained for various approximations of fractional derivatives considering these modified wave numbers fourier analysis of differencing errors is presented to quantify the resolution characteristics of various approximations a novel fourth order compact scheme is developed for space fractional advection diffusion reaction equations with variable coefficients in one and two dimensions in the proposed compact scheme the second derivative approximation of unknowns is approximated using the value of these unknowns and their first derivative approximations this splitting of second derivative approximations allows us to obtain a similar system of linear equations as in zhao and tian 2017 which presents only second order accurate finite difference method for advection diffusion reaction equations in one dimension the stability of the proposed compact scheme is demonstrated numerically furthermore the proposed compact scheme is employed to space fractional black scholes equation for pricing european options as an application of fractional derivatives in mathematical finance numerical illustrations are presented to validate the theoretical claims

a fast algorithm for testing isomorphism of permutation networks the problem of deciding whether two given permutation sequences are conjugate is addressed the author exhibits an algorithm that solves this problem in time o n log n where n is the sum of the sizes of the two sequences the algorithm can be applied to the problem of deciding whether two permutation networks are equivalent the time bound for the algorithm is a significant improvement over the o n sup 2 bound of the algorithm due to y a oruc and m y oruc 1985 the author s method applies techniques used by the hopcroft tarjan algorithm for deciding planar graph isomorphism

the universality of the shuffle exchange network this paper has focused on the realization of every arbitrary permutation with the shuffle exchange network permutation properties of shuffle exchange networks are studied and are used to demonstrate several universal networks it is concluded that 3 log2 n 1 passes through a single stage regular shuffle exchange network are sufficient to realize every arbitrary permutation where n is network size a routing algorithm is also developed to calculate control settings of the shuffle exchange switches for the permutation realization three optimal universal networks namely expanded direct connection shuffle exchange network multiple pass omega network and modified shuffle exchange network are then exploited for better interconnection purposes in addition this work specifies the inherent relationship between the shuffle exchange network and the benes binary network so that designers can have a broad prospect

picard and weakly picard operators technique for nonlinear differential equations in banach spaces abstract in this paper we study nonlocal cauchy problems for differential equations in banach spaces using picard and weakly picard operators technique and suitable bielecki norms some existence uniqueness and data dependence results are obtained under some mild conditions as an application we also discuss a class of impulsive cauchy problems by adapting the same methods

finite element approximation of optimal control problems governed by time fractional diffusion equation in this paper galerkin finite element approximation of optimal control problems governed by time fractional diffusion equations is investigated piecewise linear polynomials are used to approximate the state and adjoint state while the control is discretized by variational discretization method a priori error estimates for the semi discrete approximations of the state adjoint state and control are derived furthermore we also discuss the fully discrete scheme for the control problems a finite difference method developed in lin and xu 2007 is used to discretize the time fractional derivative fully discrete first order optimality condition is developed based on first discretize then optimize approach the stability and truncation error of the fully discrete scheme are analyzed numerical example is given to illustrate the theoretical findings

reconfiguration algorithms for interconnection networks the correspondence examines the functional relations within a class of multistage interconnection networks it is known that these networks are not rearrangeable this fact has led to some research on interconnection network relations the correspondence deals with one aspect of this research namely that of constructing an equivalence map between two interconnection networks procedures are given to test whether two such networks are equivalent whenever they are these procedures also produce a map to conjugate one network onto the other

remarks on a semilinear heat equation with integral boundary conditions abstract for a semilinear heat equation we consider a nonlocal boundary problem on the basis of the solution of a dirichlet problem for a parabolic equation and volterra integral equation we establish the well posedness for the nonlocal problem which generalizes some recent results

oscillation criteria for impulsive partial fractional differential equations in this paper we established some sufficient conditions for oscillation of solutions of a class of impulsive partial fractional differential equations with forcing term subject to robin and dirichlet boundary conditions by using differential inequality method as an application we included an example to illustrate the main result

a study of delayed cooperation diffusion system with dirichlet boundary conditions abstract in this paper we study the existence and uniqueness of strong solution of a delayed cooperation diffusion system with dirichlet boundary conditions using the method of semidiscretization in time

equivalence between functionality and topology of log n stage banyan networks existing procedures to decide network equivalence in log n stage banyan networks are based on analysis of permutations take polynomial but costly time and do not shed light on or take advantage of the relationship between functionality and topology this relationship is addressed and it is shown that two log n stage banyan networks of the same switch size are functionally equivalent if and only if they have the same underlying topology an o n log n algorithm is derived which decides if two n stage banyan networks of n inputs n outputs and r r crossbar switches as building blocks realize the same permutations the algorithm works by comparing the underlying topologies of the two networks the algorithm is optimal because the size of the networks is o n log n

zeros of classical orthogonal polynomials of a discrete variable in this paper we obtain sharp bounds for the zeros of classical orthogonal polynomials of a discrete variable considered as functions of a parameter by using a theorem of a markov and the so called hellmannfeynman theorem comparisons with previous results for zeros of hahn meixner kravchuk and charlier polynomials are also presented

on the number of permutations performable by extra stage multistage interconnection networks the number of permutations performable by extra stage multistage interconnection networks in a single pass is studied a graph theoretical approach is used to evaluate the multiplicity of the performable permutations more specifically the problem is reduced to a hypercube enumeration problem and it is shown that there is a direct correspondence between the number of partial subgraphs of a hypercube with a given number of components and the multiplicity of a corresponding class of permutations performable by the extra stage network the evaluation of these multiplicities leads to the calculation of the number of distinct permutations performable by the network

the third kind chebyshev wavelets collocation method for solving the time fractional convection diffusion equations with variable coefficients in this paper a numerical method based on the third kind chebyshev wavelets is proposed for solving a class of time fractional convection diffusion equations with variable coefficients the third kind chebyshev wavelets operational matrices of the integer order integration and the fractional order integration are derived respectively they are utilized to reduce the problem to a system of linear algebraic equations by combining the collocation method the uniform convergence analysis and error estimation for the third kind chebyshev wavelets expansion are investigated illustrative examples are given and the numerical results are presented to demonstrate the efficiency and accuracy of the proposed method

an analysis of the modified l1 scheme for time fractional partial differential equations with nonsmooth data we introduce a modified l1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous c

linear time automorphism algorithms for trees interval graphs and planar graphs an algorithm based upon edmonds s procedure for testing isomorphism of trees is extended to answer various questions concerning automorphisms of a labeled forest this and linear pattern matching techniques are used to build efficient algorithms which find the automorphism partition and a set of generators for the automorphism group determine the order of the automorphism group and compute a coding for forests interval graphs outerplanar graphs and planar graphs

a pde approach to space time fractional parabolic problems we study solution techniques for parabolic equations with fractional diffusion and caputo fractional time derivative the latter being discretized and analyzed in a general hilbert space setting the spatial fractional diffusion is realized as the dirichlet to neumann map for a nonuniformly elliptic problem posed on a semi infinite cylinder in one more spatial dimension we write our evolution problem as a quasi stationary elliptic problem with a dynamic boundary condition we propose and analyze an implicit fully discrete scheme first degree tensor product finite elements in space and an implicit finite difference discretization in time we prove stability and error estimates for this scheme

rothe s method for a telegraph equation with integral conditions abstract we study the existence and uniqueness of the solution for a telegraph equation with integral condition we apply the rothe time discretization method then we prove its convergence

rothe s method for solving some fractional integral diffusion equation abstract in this paper we apply the rothe s method to a fractional integral diffusion equation and establish the existence and uniqueness of a strong solution as an application we include an example to illustrate the main result

a method of lines for a nonlinear abstract functional evolution equation let x be a real banach space with x uniformly convex a method of lines is introduced and developed for the abstract functional problem lipschitzian like function in its two variables further conditions are given for the convergence of the method to a strong solution of e recent results for perturbed abstract ordinary equations are substantially improved the method applies also to large classes of functional parabolic problems as well as problems of integral perturbations the method is straightforward because it avoids the introduction of the operators a t and the corresponding use of nonlinear evolution operator theory 1 introduction preliminaries let x be a real banach space with norm 11 let