A Novel Algorithm for Time Fractional Advection-Diffusion Equation

被引：0
|
作者：
Zhang, Ping [1 ]
Zhang, Yingchao [1 ,2 ]
Jia, Yuntao [1 ]
Lin, Yingzhen [1 ]
机构：
[1] Beijing Inst Technol, Zhuhai Campus, Zhuhai, Guangdong, Peoples R China
[2] Zhuhai Coll Sci & Technol, Sch Data Sci, Zhuhai, Guangdong, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年
关键词：
epsilon-approximation solution; Legendre wavelets; linear interpolation; time fractional advection-diffusion equation;
D O I：
10.1002/mma.10869
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to design a discrete-continuous coupled numerical algorithm for solving a time fractional advection-diffusion equation. Firstly, we discretize time variable by linear interpolation to obtain differential equations about spatial variable. Secondly, numerical algorithm is designed to solve the above differential equations using Legendre wavelet basis constructed in the reproducing kernel space W-2(3)[0,1]. Therefore, the numerical solution of the time fractional advection-diffusion equation is obtained. Furthermore, the convergence analysis and stability analysis of the proposed algorithm have been provided. Finally, five numerical examples are proposed respectively to verify the correctness of our theoretical analysis and to demonstrate the validity and applicability of the technique.
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页数：14
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