A meshless method to solve the variable-order fractional diffusion problems with fourth-order derivative term. (October 2022)

• Record Type: Journal Article
• Authors: Safari, Farzaneh; Jing, Li; Lu, Jun; Chen, Wen
• Is Part Of: Engineering analysis with boundary elements. Volume 143(2022)
• Page Start: 677
• Page End: 686
• Publication Date: 2022-10
• Subjects: Variable-order fractional diffusion equations -- Meshless method -- Weighted and shifted difference operators -- Fourth-order fractional equation; 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.2022.07.012
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Using the meshless collocation method, a scheme for solving nonlinear variable-order fractional diffusion equations with a fourth-order derivative term is presented. Here the fractional derivative term is approximated by weighted and shifted Grünwald difference (WSGD) approximation formula. The difficulty caused by the nonlinear terms is carefully handled by quasilinearization technique. Using the radial basis functions, the solution of the problem is written in terms of the primary approximation, and the related correcting functions at each time step. Then the approximation is substituted back to the governing equations where the unknown parameters can be determined. Finally, the method is supported by several numerical experiments on irregular domains.