A meshless method in reproducing kernel space for solving variable-order time fractional advection–diffusion equations on arbitrary domain. (June 2021)

• Record Type: Journal Article
• Authors: Du, Hong; Chen, Zhong; Yang, Tiejun
• Is Part Of: Applied mathematics letters. Volume 116(2021)
• Publication Date: 2021-06
• Subjects: Variable-order time fractional differential equation -- Reproducing kernel space -- Meshless method -- Mercer kernel -- Advection–diffusion equation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.107014
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, a meshless method in reproducing kernel space is proposed for solving VOTFA-DE on arbitrary domain. Advantages of the meshless method proposed could avoid effectively difficulties of constructing shape functions using known Mercer kernel and deal with arbitrary domains. And the accuracy is verified by two examples. Highlights: The meshless method proposed could avoid effectively difficulties of constructing shape functions using known Mercer kernel. Our method can deal with arbitrary domains. Our method can be used to solve other various equations.