Journal ArticleDOI
An Improved Error Estimate for a Numerical Method for a System of Coupled Singularly Perturbed Reaction-diffusion Equations
Torsten Linss,Niall Madden +1 more
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In this paper, a central difference scheme for the numerical solution of a system of coupled reaction-diffusion equations is proposed, and it is shown that the scheme is almost second-order convergent, uniformly in the perturbation parameter.Abstract:
Abstract We consider a central difference scheme for the numerical solution of a system of coupled reaction-diffusion equations. We show that the scheme is almost second-order convergent, uniformly in the perturbation parameter. We present the results of numerical experiments to confirm our theoretical results.read more
Citations
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A brief survey on numerical methods for solving singularly perturbed problems
Mohan K. Kadalbajoo,Vikas Gupta +1 more
TL;DR: This survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems.
Journal ArticleDOI
Accurate Solution of a System of Coupled Singularly Perturbed Reaction-diffusion Equations
Torsten Linß,Niall Madden +1 more
TL;DR: A central difference scheme on layer-adapted piecewise uniform meshes is used to solve a system of coupled reaction-diffusion equations and it is shown that the scheme is almost second-order convergent, uniformly in both perturbation parameters, thus improving previous results.
Journal ArticleDOI
A uniformly convergent scheme for a system of reaction-diffusion equations
TL;DR: In this article, a system of two parabolic singularly perturbed equations of reaction-diffusion type is considered and the asymptotic behavior of the solution and its partial derivatives is given.
Journal ArticleDOI
A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term
TL;DR: In this paper, a numerical method based on finite difference scheme and Shishkin mesh for singularly perturbed two second order weakly coupled system of ordinary differential equations with discontinuous source term is presented.
Journal ArticleDOI
A coupled system of singularly perturbed parabolic reaction-diffusion equations
TL;DR: Systems with an arbitrary number of singularly perturbed parabolic reaction-diffusion equations are examined and the numerical approximations generated are shown to be uniformly convergent with respect to the singular perturbation parameters.
References
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Journal ArticleDOI
A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems
Niall Madden,Martin Stynes +1 more
TL;DR: In this paper, a coupled system of two singularly perturbed linear reaction-diffusion two-point boundary value problems is examined, where the leading term is multiplied by a small positive parameter, but these parameters may have different magnitudes.
Journal ArticleDOI
A numerical method for a system of singularly perturbed reaction-diffusion equations
TL;DR: In this article, a Dirichlet problem for a system of two coupled singularly perturbed reaction-diffusion ordinary differential equations is examined and a numerical method whose solutions converge pointwise at all points of the domain independently of the singular perturbation parameters is constructed and analyzed.
Fitted mesh methods for problems with parabolic boundary layers
TL;DR: In this article, a Dirichlet boundary value problem for a linear parabolic dierential equation is studied on a rectangular domain in the x t plane, where the coecient of the second order space derivative is a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle.
Journal ArticleDOI
Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations
TL;DR: In this paper, the first boundary value problem is considered in a strip for a system of two parabolic equations in which the parameter multiplying the highest derivatives takes arbitrary values from the half-interval (0, 1).
Journal ArticleDOI
A parameter uniform numerical method for a system of singularly perturbed ordinary differential equations
TL;DR: A parameter robust computational method is constructed and it is proved that it gives essentially first order parameter-uniform convergence in the maximum norm.
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A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems
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