A compact integrated RBF method for time fractional convection–diffusion–reaction equations. (1st May 2019)

• Record Type: Journal Article
• Authors: Qiao, Yuanyang; Zhao, Jianping; Feng, Xinlong
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 9(2019)
• Page Start: 2263
• Page End: 2278
• Publication Date: 2019-05-01
• Subjects: Time fractional convection–diffusion–reaction equation -- CIRBF method -- Shifted Grünwald formula -- Stability and convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.12.017
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, a local compact integrated radial basis function (CIRBF) method is proposed to solve the time fractional convection–diffusion–reaction equations. The proposed CIRBF scheme derives high accuracy and fast convergence rate with grid refinement. The spatial derivatives are discretized by combining with the integrated RBF approximation and compact approximation in a stencil. The nodal function values and the nodal second derivatives are used to establish the relation between the physical space and the RBF weight space. The time discretization is replaced by the second order shifted Grünwald scheme. Moreover, the unconditional stability and convergence of the proposed method are shown. Finally, some numerical examples on 2D and 3D domains are carried out to verify the accuracy and efficiency of the proposed algorithm for the fractional differential equations.