Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution

被引：4

作者：

Kedia, Nikki ^{[1
]}

Alikhanov, Anatoly A. ^{[2
]}

Singh, Vineet Kumar ^{[1
]}

机构：

[1] Banaras Hindu Univ, Indian Inst Technol, Dept Math Sci, Varanasi, India

[2] North Caucasus Fed Univ, North Caucasus Ctr Math Res, Stavropol, Russia

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2024年 / 219卷

基金：

俄罗斯科学基金会;

关键词：

Fractional derivative with generalized memory; kernel; Non-smooth solution; Weight function; Non-linear; Generalized L1 scheme; Convergence and stability; NUMERICAL APPROXIMATION; SUBDIFFUSION; CONVERGENCE; MESHES;

D O I：

10.1016/j.matcom.2023.12.034

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The present paper aims to develop a stable multistep numerical scheme for the non-linear generalized time -fractional diffusion equations (GTFDEs) with non -smooth solutions. Mesh grading technique is used to discretize the temporal direction, which results in 2 - alpha order of convergence (0 < alpha < 1). The spatial direction is discretized using a second order difference operator and the non-linear term is approximated using Taylor's series. Theoretical stability and convergence analysis is established in the L-2-norm. Moreover, some random noise perturbations are added to investigate the numerical stability of the developed scheme. Finally, numerical simulations are performed on three test examples to verify the robustness and efficiency of the scheme.

引用

页码：337 / 354

页数：18