An interpolating meshless method for the numerical simulation of the time-fractional diffusion equations with error estimates
ISSN: 0264-4401
Article publication date: 19 August 2019
Issue 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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