Journal of Mathematical Chemistry

, Volume 52, Issue 8, pp 2030–2051

A new efficient technique for solving two-point boundary value problems for integro-differential equations

  • Randhir Singh
  • Gnaneshwar Nelakanti
  • Jitendra Kumar
Original Paper

DOI: 10.1007/s10910-014-0363-8

Cite this article as:
Singh, R., Nelakanti, G. & Kumar, J. J Math Chem (2014) 52: 2030. doi:10.1007/s10910-014-0363-8

Abstract

In this paper, we propose a new efficient method based on a combination of Adomian decomposition method (ADM) and Green’s function for solving second-order boundary value problems (BVPs) for integro-differential equations (IDEs). The proposed method depends on constructing Green’s function before establishing the recursive scheme for the solution components. Unlike the ADM or modified ADM , the proposed method avoids solving a sequence of difficult nonlinear equations (transcendental equations) for the unknown parameters. The proposed method provides a direct recursive scheme for obtaining the series solution with easily calculable components. We also provide a sufficient condition that guarantees a unique solution to the second-order BVPs for IDEs. Convergence and error analysis of the proposed method are also discussed. Convergence analysis is reliable enough to estimate the error bound of the series solution. Some numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed approach. The numerical results reveal that the proposed method is very effective and simple.

Keywords

Integro-differential equations Boundary value problems Adomian decomposition method Green’s function Approximations 

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Randhir Singh
    • 1
  • Gnaneshwar Nelakanti
    • 1
  • Jitendra Kumar
    • 1
  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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