Efficient hybrid group iterative methods in the solution of two-dimensional time fractional cable equation

Advances in Difference Equations

article

Salama, Fouad Mohammad¹  Hj. Mohd. Ali, Norhashidah¹  Abd Hamid, Nur Nadiah¹ 

[1] School of Mathematical Sciences, Universiti Sains Malaysia

关键词: Caputo fractional derivative;    Time-fractional derivative;    Cable equation;    Laplace transform;    Finite differences;    Group iterative methods;    Stability and convergence analyses;   

DOI  :  10.1186/s13662-020-02717-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, the development of new hybrid group iterative methods for the numerical solution of a two-dimensional time-fractional cable equation is presented. We use Laplace transform method to approximate the time fractional derivative which reduces the problem into an approximating partial differential equation. The obtained partial differential equation is solved by four-point group iterative methods derived from two implicit finite difference schemes. Matrix norm analysis together with mathematical induction are utilized to investigate the stability and convergence properties. A comparative study with the recently developed hybrid standard point (HSP) iterative method accompanied by their computational cost analysis are also given. Numerical experiments are conducted to demonstrate the superiority of the proposed hybrid group iterative methods over the HSP iterative method in terms of the number of iterations, computational cost as well as the CPU times.

【 授权许可】

CC BY