A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms

被引：87

作者：

Chandru, M. ^{[1
,2
]}

Prabha, T. ^{[1
]}

Das, P. ^{[3
]}

Shanthi, V. ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Tiruchirappalli 620015, Tamil Nadu, India

[2] Vignans Univ, Dept Math, Vadlamudi, Andhra Pradesh, India

[3] Indian Inst Technol Patna, Dept Math, Patna 801103, Bihar, India

来源：

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2019年 / 27卷 / 1-3期

关键词：

Boundary and interior layers; Parabolic partial differential equation; Initial boundary value problem; Time dependent problem; Singular perturbation; Reaction-convection-diffusion; Two-parameter problem; Parameter uniform numerical method; 35G05; 35G16; 35K20; 35K51; 65M06; 65M50; 65M12; DIFFERENTIAL-EQUATION; DIFFUSION PROBLEMS; SCHEME;

D O I：

10.1007/s12591-017-0385-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a parameter uniform numerical method is developed for a two-parameter singularly perturbed parabolic partial differential equation with discontinuous convection coefficient and source term. The presence of perturbation parameter and the discontinuity in the convection coefficient and source term lead to the boundary and interior layers in the solution. On the spatial domain, an adaptive mesh is introduced before discretizing the continuous problem. The present method observes a uniform convergence in maximum norm which is almost first-order in space and time irrespective of the relation between convection and diffusion parameters. Numerical experiment is carried out to validate the present scheme.

引用

页码：91 / 112

页数：22

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