Abstract
Abstract In this paper, a singularly perturbed differential equation with a large delay is considered. The considered problem contains a large delay parameter on the reaction term. The solution of the problem exhibits the interior layer due to the delay parameter and the strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using the fitted non-polynomial spline method. The stability and parameter uniform convergence of the proposed method is proved. To validate the applicability of the scheme, two model problems of the variable coefficient are considered for numerical experimentation.
Highlights
A differential equation is said to be a 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 a fitted non-polynomial cubic spline method for singularly perturbed differential equations with a large delay
The numerical scheme is developed on the uniform mesh using a fitted operator in the given differential equation
Summary
A differential equation is said to be a 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. The authors of [5,6,7] have developed various numerical schemes on uniform meshes for singularly perturbed second-order differential equations having a small delay on convection term. In the present paper, motivated by the works of [8,9,10,11,12], we developed a fitted non-polynomial spline method for the numerical solution of second-order singularly perturbed convection–diffusion equations with large delay.
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