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

Document Type : Research Paper


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


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.


Volume 14, Issue 1
January 2023
Pages 1481-1498
  • Receive Date: 30 September 2021
  • Revise Date: 29 August 2022
  • Accept Date: 17 September 2022