An Implicit Numerical Method for Semilinear Space-Time Fractional Diffusion Equation

Gunvant Achutrao BIRAJDAR

Authors

Gunvant Achutrao BIRAJDAR Tata Institute of Social Sciences Tuljapur Campus, Tuljapur, Dist: Osmanabad (M.S.) 413601

Keywords:

Riemann-Liouville fractional derivative, Caputo fractional derivative, implicit finite difference method, stability, convergence

Abstract

The aim of the study is to obtain the solution of semilinear space-time fractional diffusion equation for the first initial boundary value problem (IBVP), by applying an implicit method. The main idea of the method is to convert the problem into an algebraic system which simplifies the computations. We discuss the stability, convergence and error analysis of the implicit finite difference scheme with suitable example using MATLAB.

doi:10.14456/WJST.2015.40

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