Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

Year 2019, Volume: 11 Issue: 4, 476 - 493, 05.12.2019

Habtamu Garoma Debela , Gemechis File Duressa

https://doi.org/10.24107/ijeas.647640

Cited By: 4

Abstract

In this paper, exponentially fitted finite difference method for
solving singularly perturbed delay differential equation with integral boundary
condition is considered. To treat the integral boundary condition, Simpson’s
rule is applied. The stability and parameter uniform convergence of the
proposed method are proved. To validate the
applicability of the scheme, two model problems are considered for
numerical experimentation and solved for different values of the perturbation
parameter,  and mesh size,  The numerical
results are tabulated in terms of maximum absolute errors and rate of
convergence and it is observed that the present method is more accurate and -uniformly convergent for  where the
classical numerical methods fails to give good result and it also improves the
results of the methods existing in the literature.

Keywords

Singularly perturbed problems, Delay differential equation, Exponentially fitted operator, Integral boundary condition

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