An approximation approach towards a class of integro-differential equation with pure delay

Sarkar, Nimai; Sen, Mausumi; Saha, Dipankar; Agarwal, Ravi

doi:10.22075/ijnaa.2022.24683.2803

An approximation approach towards a class of integro-differential equation with pure delay

Document Type : Research Paper

Authors

Nimai Sarkar ¹

Mausumi Sen ²

Dipankar Saha ³

Ravi Agarwal ⁴

¹ Department of Mathematics, Madanapalle Institute of Technology & Science, India

² Department of Mathematics, National Institute of Technology Silchar, India

³ Department of Mathematics, DRK Institute of Science and Technology, Hyderabad, India

⁴ Department of Mathematics, Texas A & M University-Kingsville, Texas, 78363-8202, USA

10.22075/ijnaa.2022.24683.2803

Abstract

In this article, we study a new numerical approach to solve some particular class of delay integro-differential equations. The considered problem is a singularly perturbed Volterra integro-differential equation with a pure delay term. To solve such equations numerically we adopt the standard Adomian decomposition method followed by a first-order truncated Taylor approximation. The most appealing advantage of the present method is that it provides an adequate result for a wide scale of values to the perturbation parameter. The efficiency of the proposed method is illustrated with an example. Moreover, a vivid realization of the treatment is described by the theoretical study related to error analysis. Under some relevant assumptions boundedness of solution, and stability analysis are also established in the agreement of the current method. To strengthen our findings, a comparative study between the proposed technique and the well-renowned spline method is presented in the manuscript. Moreover, outcomes suggest the prior efficiency of the method which is also supported by the theoretical results.

Keywords

Volterra integro-differential equation

Adomian Decomposition

Hyer-Ulam-Rassias stability