A new semi-analytical collocation method for solving multi-term fractional partial differential equations with time variable coefficients

作者：Reutskiy, S. Yu.^*

来源：Applied Mathematical Modelling, 2017, 45: 238-254.

DOI：10.1016/j.apm.2016.12.029

• Time fractional equations
• Numerical solution
• Wave-diffusion equation
• Time-fractional telegraph equation
• Fractional sub-diffusion equations

The aim of this paper is to present a new numerical method for solving a wide class of fractional partial differential equations (FPDEs) such as wave-diffusion equations, modified anomalous fractional sub-diffusion equations, time-fractional telegraph equations. The proposed method is based on the Fourier series expansion along the spatial coordinate which transforms the original equation into a sequence of multi-term fractional ordinary differential equations (ODEs). These fractional equations are solved by the use of a new efficient numerical technique the backward substitution method. The numerical examples confirm the high accuracy and efficiency of the proposed numerical scheme in solving FPDEs with variable in time coefficients.

• 出版日期2017-5
• 单位河海大学