An intelligent non-uniform mesh to improve errors of a stable numerical method for time-tempered fractional advection-diffusion equation with weakly singular solution

被引：0

作者：

Ahmadinia, Mahdi ^{[1
]}

Abbasi, Mokhtar ^{[1
]}

Hadi, Parisa ^{[1
]}

机构：

[1] Univ Qom, Dept Math, POB 37185 3766, Qom, Iran

来源：

JOURNAL OF SUPERCOMPUTING | 2024年 / 80卷 / 18期

关键词：

Advection-diffusion equation; Tempered fractional derivative; Finite volume element method; Weakly singular; Non-uniform mesh; Parallel computing; Stability; FINITE-DIFFERENCE METHOD; DISPERSION EQUATION; ELEMENT-METHOD; RANDOM-WALKS; LEVY MOTION; MEDIA;

D O I：

10.1007/s11227-024-06442-w

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper introduces a finite volume element method for solving the time-tempered fractional advection-diffusion equation with weakly singular solution at initial time t=0. An innovative approach is proposed to construct an intelligent non-uniform temporal mesh, which significantly reduces errors as compared to using a uniform temporal mesh. The error reduction is quantified in terms of percentage improvement of errors. Due to the presence of a large number of integral calculations involving complicated functions, we used parallel computing techniques to accelerate the computation process. The stability of the method is rigorously proven, and numerical examples are provided to demonstrate the effectiveness of the method and validate the theoretical results.

引用

页码：26280 / 26307

页数：28

共 28 条

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[8] Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions
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