Journal ArticleDOI
A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition
P. Avudai Selvi,N. Ramanujam +1 more
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TLDR
A numerical method comprising a standard finite difference scheme on a rectangular piecewise uniform fitted mesh of Nx × Nt elements condensing in the boundary layers is suggested and it is proved to be parameter-uniform.About:
This article is published in Applied Mathematics and Computation.The article was published on 2017-03-01. It has received 21 citations till now. The article focuses on the topics: Robin boundary condition & Method of matched asymptotic expansions.read more
Citations
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Journal ArticleDOI
Numerical treatment of two-parameter singularly perturbed parabolic convection diffusion problems with non-smooth data
Journal ArticleDOI
Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions
Sunil Kumar,Sumit,Higinio Ramos +2 more
TL;DR: This work develops a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions and proves that the method is parameter- uniformly convergent of order two in space and order one in time.
Journal ArticleDOI
Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition
Sekar Elango,A. Tamilselvan,R. Vadivel,Nallappan Gunasekaran,Haitao Zhu,Jinde Cao,Jinde Cao,Xiaodi Li +7 more
TL;DR: In this article, singularly perturbed parabolic partial differential equations with delay in space were investigated, and the right end plane is an integral boundary condition on a rectangular domain, and a small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain.
Journal ArticleDOI
A Uniformly Convergent Collocation Method for Singularly Perturbed Delay Parabolic Reaction-Diffusion Problem
TL;DR: In this article, a numerical solution is proposed for singularly perturbed delay parabolic reaction-diffusion problem with mixed-type boundary conditions, which is discretized by the implicit Euler method on uniform mesh in time and extended cubic B-spline collocation method on Shishkin mesh in space.
Journal ArticleDOI
Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline
TL;DR: A numerical technique for a class of singularly perturbed time delayed parabolic partial differential equation and a priori results of maximum principle, stability and bounds are discussed.
References
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Book
Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
Book
Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems
TL;DR: In this article, the analytical behavior of solutions for second-order boundary value problems and higher-order problems was analyzed. But the analytical behaviour of solutions was not analyzed for the first order boundary value problem.
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A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations
TL;DR: In this article, a Dirichlet boundary value problem for a delay parabolic differential equation is studied on a rectangular domain in the x-t plane, where the second-order space derivative is multiplied by a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle.
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ε-uniform schemes with high-order time-accuracy for parabolic singular perturbation problems
TL;DR: This paper develops schemes for which the order of convergence in time can be arbitrarily large if the solution is sufficiently smooth, and uses a mesh with nodes that are condensed in the neighbourhood of the boundary layers to obtain uniform convergence.
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.