Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition

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Department of Mathematics, Jimma University, P. O. Box 378, Jimma, Ethiopia

Abstract

n this paper, accelerated fitted finite difference method for solving singularly perturbed
delay differential equation with non-local boundary condition is considered. To treat the
non-local boundary condition, Simpson’s rule is applied. The stability and parameter
uniform convergence for 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 ε and mesh size h. 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 ε-uniformly convergent for h ≥ ε
where the classical numerical methods fails to give good result, and it also improves the
results of the methods existing in the literature.

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