Two tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Padé approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM), then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.
SUMMARYIn this paper, numerical solution of partial differential equations (PDEs) is considered by multivariate padé approximations. We applied these method to two examples. First, PDE has been converted to power series by two-dimensional differential transformation, Then the numerical solution of equation was put into multivariate padé series form. Thus, we obtained numerical solution of PDE.
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.
In this paper, univariate Pade approximation is applied to fractional power
sries solutions of fractional integro-differential equations with
non-local boundary conditions. As it is seen from comparisons, univariate
Pade approximation gives reliable solutions and numerical results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.