Comparing Numerical Methods for Solving Time-Fractional Reaction-Diffusion Equations

Abstract

Multivariate Padé approximation (MPA) is applied to numerically approximate the solutions of time-fractional reaction-diffusion equations, and the numerical results are compared with solutions obtained by the generalized differential transform method (GDTM). The fractional derivatives are described in the Caputo sense. Two illustrative examples are given to demonstrate the effectiveness of the multivariate Padé approximation (MPA). The results reveal that the multivariate Padé approximation (MPA) is very effective and convenient for solving time-fractional reaction-diffusion equations.

Rational approximations for solving cauchy problems

“…In recent times, univariate and multivariate padé approximaton have been succesfully applied to various problems in physical and engineering sciences [1][2][3][4][5]. "Padé approximant represents a function by the ratio of two polynomials.…”

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

“…Many definitions and theorems have been developed for multivariate Padé approximations MPA (see [15] for a survey on multivariate Padé approximation). The multivariate Padé Approximation has been used to obtain approximate solutions of linear or nonlinear differential equations [16][17][18][19].…”

“…( , ) = ( 2 + 0.7500000002 × 10 −9 ) 2 + 0.7500000002 × 10 −9 . (20)For = 0.5(17) is ( , ) = 1.128379167 0.5 − 0.95779798501.5 + 0.6018022226 2.5 − 0.70056081163.5 . (21)For simplicity, let1/2 = ; then ( , ) = 1.128379167 − 0.9577979850 3 + 0.6018022226 5 − 0.7005608116 7 .…”

Multivariate Padé Approximations For Solving Nonlinear Diffusion Equations

“…In recent times,univariate and multivariate Padé approximation have been successfully applied to various problems in physical and engineering sciences [1][2][3][4][5][6][7]. As it is indicated in [16] "a Padé approximation can be far more accurate than a Taylor approximation.…”