Stable and Convergent Finite Difference Schemes on NonuniformTime Meshes for Distributed-Order Diffusion Equations

被引：0

作者：

Morgado, M. Luisa ^{[1
,2
]}

Rebelo, Magda ^{[3
]}

Ferras, Luis L. ^{[4
]}

机构：

[1] Univ Lisbon, Ctr Computat & Stochast Math, Inst Super Tecn, P-1049001 Lisbon, Portugal

[2] Univ Tras Os Montes & Alto Douro, Dept Math, UTAD, P-5001801 Vila Real, Portugal

[3] FCT NOVA, NOVA Sch Sci & Technol, Dept Math, Ctr Math & Applicat CMA, P-2829516 Quinta Da Torre, Caparica, Portugal

[4] Univ Minho, Ctr Math CMAT, Campus Azurem, P-4800058 Guimaraes, Portugal

来源：

MATHEMATICS | 2021年 / 9卷 / 16期

关键词：

distributed-order derivatives; finite differences; diffusion equations; nonuniform meshes; stability; convergence; TIME-FRACTIONAL DIFFUSION; WAVE EQUATION; APPROXIMATION;

D O I：

10.3390/math9161975

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than the use of a uniform mesh, in the case of nonsmooth solutions.

引用

页数：15

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