ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS

被引：0

作者：

Linss, Torsten ^{[1
]}

Madden, Niall ^{[2
]}

机构：

[1] Tech Univ Dresden, Inst Numer Math, D-01062 Dresden, Germany

[2] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2010年 / 7卷 / 03期

关键词：

reaction-dirusion problems; layer-adapted meshes; alternating directions; singular perturbation; UNIFORM-CONVERGENCE; PARAMETER; SCHEME; MESH;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an analysis of an Alternating Direction Implicit (ADI) scheme for a linear, singularly perturbed reaction-diffusion equation. By providing an expression for the error that separates the temporal and spatial components, we can use existing results for steady-state problems to give a succinct analysis for the time-dependent problem, and that generalizes for various layer-adapted meshes. We report the results of numerical experiments that support the theoretical findings. In addition, we provide a numerical comparison between the ADI and Euler techniques, as well details of the computational advantage gained by parallelizing the algorithm.

引用

页码：507 / 519

页数：13

共 50 条

[31] Breathing pulses in singularly perturbed reaction-diffusion systems
Veerman, Frits
NONLINEARITY, 2015, 28 (07) : 2211 - 2246
[32] An Analysis of the Robust Convergent Method for a Singularly Perturbed Linear System of Reaction-Diffusion Type Having Nonsmooth Data
Chawla, Sheetal
Singh, Jagbir
Urmil
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2022, 19 (01)
[33] Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems
Zhu, Guoqing
Chen, Shaochun
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (10) : 3048 - 3063
[34] A Novel Method for Singularly Perturbed Delay Differential Equations of Reaction-Diffusion Type
P. Pramod Chakravarthy
Kamalesh Kumar
Differential Equations and Dynamical Systems, 2021, 29 : 723 - 734
[35] ON THE SINGULARLY PERTURBED SEMILINEAR REACTION-DIFFUSION PROBLEM AND ITS NUMERICAL SOLUTION
Vulanovic, Relja
Teofanov, Ljiljana
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2016, 13 (01) : 41 - 57
[36] A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
Linss, Torsten
APPLICATIONS OF MATHEMATICS, 2014, 59 (03) : 241 - 256
[37] A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
Torsten Linss
Applications of Mathematics, 2014, 59 : 241 - 256
[38] Convergence analysis of the LDG method applied to singularly perturbed problems
Zhu, Huiqing
Zhang, Zhimin
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (02) : 396 - 421
[39] Approximation of singularly perturbed reaction-diffusion problems by quadratic C1-splines
Linss, Torsten
Radojev, Goran
Zarin, Helena
NUMERICAL ALGORITHMS, 2012, 61 (01) : 35 - 55
[40] Uniform convergence of discontinuous finite element methods for singularly perturbed reaction-diffusion problems
Li, JC
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 44 (1-2) : 231 - 240

← 1 2 3 4 5 →