Abstract
In 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.
Highlights
A differential equation is said to be singularly perturbed delay differential equation, if it includes at least one delay term, involving unknown functions occurring with different arguments, and the highest derivative term is multiplied by a small parameter
This study introduces accelerated fitted operator numerical method for solving singularly perturbed delay differential equations with integral boundary condition
The numerical scheme is developed on uniform mesh using fitted operator finite difference method in the given differential equation
Summary
A differential equation is said to be singularly perturbed delay differential equation, if it includes at least one delay term, involving unknown functions occurring with different arguments, and the highest derivative term is multiplied by a small parameter. Finding the solution of singularly perturbed delay differential equations, whose application mentioned above, is a challenging problem. Debela and Duressa Journal of the Egyptian Mathematical Society (2020) 28:16 numerical schemes on uniform meshes for singularly perturbed first and second order differential equations with integral boundary conditions.
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