A finite point method for the fractional cable equation using meshless smoothed gradients. (1st January 2022)

• Record Type: Journal Article
• Authors: Li, Xiaolin; Li, Shuling
• Is Part Of: Engineering analysis with boundary elements. Volume 134(2022)
• Page Start: 453
• Page End: 465
• Publication Date: 2022-01-01
• Subjects: Meshless methods -- Finite point method -- Stabilized moving least squares approximation -- Meshless smoothed gradient -- Fractional cable equation -- Error estimation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.10.018
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper presents a meshless finite point method (FPM) for the numerical analysis of the fractional cable equation. A second-order time discrete scheme is proposed to approximate both integer-order and fractional-order time derivatives. Then, based on the stabilized moving least squares approximation and the meshless smoothed gradients, a new implementation of the FPM is provided to enhance the accuracy and convergence rate in space. Theoretical error of the FPM is analyzed. Numerical results verify the efficiency of the method and show that the method can gain second-order accuracy in time and fourth-order accuracy in space.