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

共 50 条

[1] Two unconditionally stable and convergent difference schemes with the extrapolation method for the one-dimensional distributed-order differential equations
Gao, Guang-hua
Sun, Zhi-zhong
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016, 32 (02) : 591 - 615
[2] Finite Difference/Finite Element Methods for Distributed-Order Time Fractional Diffusion Equations
Weiping Bu
Aiguo Xiao
Wei Zeng
Journal of Scientific Computing, 2017, 72 : 422 - 441
[3] Some high-order difference schemes for the distributed-order differential equations
Gao, Guang-hua
Sun, Hai-wei
Sun, Zhi-zhong
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 298 : 337 - 359
[4] Finite Difference/Finite Element Methods for Distributed-Order Time Fractional Diffusion Equations
Bu, Weiping
Xiao, Aiguo
Zeng, Wei
JOURNAL OF SCIENTIFIC COMPUTING, 2017, 72 (01) : 422 - 441
[5] Introducing Graded Meshes in the Numerical Approximation of Distributed-order Diffusion Equations
Morgado, M. L.
Rebelo, M.
NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA-2016), 2016, 1776
[6] Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations
Gao, Guang-hua
Sun, Zhi-zhong
JOURNAL OF SCIENTIFIC COMPUTING, 2016, 66 (03) : 1281 - 1312
[7] Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations
Guang-hua Gao
Zhi-zhong Sun
Journal of Scientific Computing, 2016, 66 : 1281 - 1312
[8] Two difference schemes for solving the one-dimensional time distributed-order fractional wave equations
Gao, Guang-hua
Sun, Zhi-zhong
NUMERICAL ALGORITHMS, 2017, 74 (03) : 675 - 697
[9] Space-time finite element method for the distributed-order time fractional reaction diffusion equations
Bu, Weiping
Ji, Lun
Tang, Yifa
Zhou, Jie
APPLIED NUMERICAL MATHEMATICS, 2020, 152 : 446 - 465
[10] CONVERGENT FINITE DIFFERENCE SCHEMES FOR STOCHASTIC TRANSPORT EQUATIONS
Fjordholm, Ulrik S.
Karlsen, Kenneth H.
Pang, Peter H. C.
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2025, 63 (01) : 149 - 192

← 1 2 3 4 5 →