Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

Authors

  • Dimple Rani Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India.
  • Vinod Mishra Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India.

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.2645

Keywords:

Numerical Laplace Transform Method, Volterra Integral Equations(VIEs), Volterra Integro-differential Equations(VIDEs), Adomian Decomposition Method(ADM), Newton Raphson formula.

Abstract

In this paper, we establish a modified Laplace decomposition method for nonlinear volterra integral and integro-differential equations. This technique differs from the general Laplace decomposition method because of the terms involved in Adomian polynomial.We have used Newton Raphson formula in place of the $u_{i}$ in Adomian polynomial. The proposed scheme is investigated with some illustrative examples and has given reliable results.

Author Biographies

  • Dimple Rani, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India.

    Department of Mathematics,

    Ph.D Research Schloar

  • Vinod Mishra, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India.

    Department of Mathematics,

    Professor

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Published

2018-01-30

Issue

Vol. 11 No. 1: (January 2018)

Section

Approximation Theory

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How to Cite

Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula. (2018). European Journal of Pure and Applied Mathematics, 11(1), 202-214. https://doi.org/10.29020/nybg.ejpam.v11i1.2645