Premium
Uniformly convergent numerical method for singularly perturbed differential‐difference equation using grid equidistribution
Author(s) -
Mohapatra Jugal,
Natesan Srinivasan
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1370
Subject(s) - mathematics , norm (philosophy) , mathematical analysis , uniform convergence , grid , singular perturbation , numerical analysis , exact solutions in general relativity , differential equation , perturbation (astronomy) , finite difference , finite difference method , geometry , computer science , computer network , physics , bandwidth (computing) , quantum mechanics , political science , law
In this paper, a class of singularly perturbed differential‐difference equations with small delay and shift terms is considered. A numerical method comprising of upwind finite difference operator on an adaptive grid, which is formed by equidistributing the arc‐length monitor function, is constructed for approximating the solution. The method is proved to be robust, in the sense that the discrete solution obtained converges in the maximum norm to the exact solution uniformly with respect to the perturbation parameter. Parameter‐uniform error bounds for the numerical approximations are established. Numerical examples support the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.