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An interpolating meshless method for the numerical simulation of the time-fractional diffusion equations with error estimates

Jufeng Wang (College of Finance and Information, Ningbo University of Finance and Economics, Ningbo, China, and Ningbo Institute of Technology, Zhejiang University, Ningbo, China)
Fengxin Sun (Faculty of Science, Ningbo University of Technology, Ningbo, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 19 August 2019

Abstract

Purpose

This paper aims to present an interpolating element-free Galerkin (IEFG) method for the numerical study of the time-fractional diffusion equation, and then discuss the stability and convergence of the numerical solutions.

Design/methodology/approach

In the time-fractional diffusion equation, the time fractional derivatives are approximated by L1 method, and the shape functions are constructed by the interpolating moving least-squares (IMLS) method. The final system equations are obtained by using the Galerkin weak form. Because the shape functions have the interpolating property, the unknowns can be solved by the iterative method after imposing the essential boundary condition directly.

Findings

Both theoretical and numerical results show that the IEFG method for the time-fractional diffusion equation has high accuracy. The stability of the fully discrete scheme of the method on the time step is stable unconditionally with a high convergence rate.

Originality/value

This work will provide an interpolating meshless method to study the numerical solutions of the time-fractional diffusion equation using the IEFG method.

Keywords

Acknowledgements

This work is supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY18A010003), the National Natural Science Foundation of China (Grant No. 11702153) and the Natural Science Foundation of Ningbo City (Grant No. 2018A610196).

Citation

Wang, J. and Sun, F. (2019), "An interpolating meshless method for the numerical simulation of the time-fractional diffusion equations with error estimates", Engineering Computations, Vol. 37 No. 2, pp. 730-752. https://doi.org/10.1108/EC-03-2019-0117

Publisher

:

Emerald Publishing Limited

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