An interpolating meshless method for the numerical simulation of the time-fractional diffusion equations with error estimates. Issue 2 (19th August 2019)

• Record Type: Journal Article
• Authors: Wang, Jufeng; Sun, Fengxin
• Is Part Of: Engineering computations. Volume 37:Issue 2(2020)
• Page Start: 730
• Page End: 752
• Publication Date: 2019-08-19
• Subjects: Fractional derivative -- Error estimate -- Time-fractional diffusion equation -- Interpolating element-free Galerkin (IEFG) method -- Interpolating moving least-squares (IMLS) method; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-03-2019-0117
• Languages: English
• ISSNs: 0264-4401

Abstract

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.