A parameter uniform convergence for a system of two singularly perturbed initial value problems with different perturbation parameters and Robin initial conditions
Downloads
Abstract
In this paper an initial value problem for a system of two singularly perturbed first order differential equations with
different perturbation parameters and Robin initial conditions is considered on the interval (0;1]. A numerical
method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested.
This method is proved to be first - order convergent in the maximum norm uniformly in the perturbation parameters.
A numerical illustration is provided to support the theory.
Keywords:
Singular perturbation problems, different perturbation parameters, Robin initial conditions, Finite difference schemes, Shishkin mesh, Parameter uniform convergenceMathematics Subject Classification:
Mathematics- Pages: 498-505
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
H.G.Roos, M.Stynes and L.Tobiska. Numerical Methods for Singularly Perturbed Differential Equations. Springer Verlag, 1996.
J.J.H. Miller, E.O'Riordan, and G.I. Shishkin. Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions. World Scientific publishing Co.Pvt.Ltd., Singapore, 1996.
R. E. O'Malley. Introduction to Singular Perturbations. Academic Press, New York, 1974.
E. P. Doolan, J.J.H. Miller, W. H. A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, 1980.
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E.O'Riordan, and G.I.Shishkin. Robust computational techniques for boundary layers. Chapman and hall/CRC, Boca Raton, Florida,USA, 2000.
P. Maragatha Meenakshi, S. Valarmathi, and J.J.H. Miller. Solving a partially singularly perturbed initial value problem on shishkin meshes. Applied Mathematics and Computation, 215:3170-3180, 2010.
S. Valarmathi and J.J.H. Miller. A parameter-uniform finite difference method for a singularly perturbed initial value problem: a special case. Lecture notes in Computational Science and Engineering, Springer-Verlag, 29:267276, 2009.
N. Shivaranjani, N.Ramanujam, J.J.H. Miller, and S. Valarmathi. A parameter uniform method for an initial value problem for a system of singularly perturbed delay differential equations. Springer proceedings in Mathematics and Statistics, 87:127-138, 2014.
Sonlin Chen, Weigen Hou, Xiaohui Jiang, Finite element analysis for singularly perturbed advection- diffusion Robin boundary values problem, Advances in Pure Mathematics, No.3,pp 643-646 (2013).
Ni Shou Ping, Diagonalization method for a singularly perturbed vector Robin problem, Applied Mathematics and Mechanics, Volume 10, 329-336, (1989).
Janet Rajaiah, Valarmathi Sigamani, A ParameterUniform Essentially First Order Convergent Fitted Mesh Method for a Singularly Perturbed Robin Problem, International Journal of Mathematics Trends and Technology (IJMTT) - Volume 59, Number 1- July 2018.
Similar Articles
- P. Roushini Leely Pushpam, M. Kamalam, Weak Roman domination in Chess graphs , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
