A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains

被引：70

作者：

Fu, Zhuo-Jia ^{[1
,2
,3
]}

Reutskiy, Sergiy ^{[2
]}

Sun, Hong-Guang ^{[2
]}

Ma, Ji ^{[2
]}

Khan, Mushtaq Ahmad ^{[4
]}

机构：

[1] Hohai Univ, Minist Educ, Key Lab Coastal Disaster & Def, Nanjing 210098, Jiangsu, Peoples R China

[2] Hohai Univ, Coll Mech & Mat, Ctr Numer Simulat Software Engn & Sci, Nanjing 211100, Jiangsu, Peoples R China

[3] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

[4] Univ Engn & Technol Mardan, Khyber Pakhtunkhwa 23200, Pakistan

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 94卷

关键词：

Variable-order time fractional derivation; Kernel-based solver; Radial basis functions; Muntz polynomials; DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; COLLOCATION METHOD; DIFFUSION; SCHEME; TERM; SUBDIFFUSION;

D O I：

10.1016/j.aml.2019.02.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study presents a robust kernel-based collocation method (KBCM) for solving multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method, Radial basis functions (RBFs) and Muntz polynomials basis (MPB) are implemented to discretize the spatial and temporal derivative terms in the VOTFPDEs, respectively. Due to the properties of the RBR, the spatial discretization in the proposed method is mathematically simple and truly meshless, which avoids troublesome mesh generation for high-dimensional problems involving irregular geometries. Due to the properties of the MPB, only few temporal discretization is required to achieve the satisfactory accuracy. Numerical efficiency of the proposed method is investigated under several typical examples. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：105 / 111

页数：7

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