TITLE:
Laplace Discrete Adomian Decomposition Method for Solving Nonlinear Integro Differential Equations
AUTHORS:
H. O. Bakodah, M. Al-Mazmumy, S. O. Almuhalbedi, Lazim Abdullah
KEYWORDS:
Integro-Differential Equation, Volterra Integro-Differential Equation, Fredholm Integro-Differential Equation, Laplace Adomian Decomposition Method, Quadrature Rules
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.6,
June
30,
2019
ABSTRACT: This paper proposes the Laplace Discrete Adomian
Decomposition Method and its application for solving nonlinear integro-differential equations. This method is
based upon the Laplace Adomian decomposition method coupled with some
quadrature rules of numerical integration. Four numerical examples of integro-differential
equations in both Volterra and Fredholm integrals are used to be solved by the
proposed method. The performance of the proposed method is verified through
absolute error measures between the approximated solutions and exact solutions.
The series of experimental numerical results show that our proposed method performs in high accuracy and efficiency. The study clearly highlights that the proposed
method could be used to overcome the analytical approaches in solving nonlinear integro-differential equations.