Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations

Volume 21, Issue 2, pp 158--163 http://dx.doi.org/10.22436/jmcs.021.02.07

Publication Date: April 16, 2020 Submission Date: February 09, 2020 Revision Date: February 28, 2020 Accteptance Date: March 03, 2020

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Authors

Lafta A. Dawood - Department of Mathematics, Thi Qar Directorates of Education, Ministry of Education, Iraq. Ahmed A. Hamoud - Department of Mathematics, Faculty of Education and Science, Taiz University, Taiz, Yemen. Nedal M. Mohammed - Department of Computer Science, Faculty of Education and Science, Taiz University, Taiz, Yemen.

Abstract

In this article, a new modification of the Adomian Decomposition Method (ADM) that is called the Laplace Discrete Adomian Decomposition Method (LDADM) is applied to non-homogeneous nonlinear Volterra-Fredholm integro-differential equations. This method is based upon the Laplace Adomian decomposition method coupled with some quadrature rules of numerical integration. 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 highlights that the proposed method could be used to overcome the analytical approaches in solving nonlinear Volterra-Fredholm integro-differential equations.

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Keywords

• Volterra-Fredholm integro-differential equation
• Adomian decomposition method
• Laplace transform
• absolute error
• approximated solution

MSC

•  45J05
•  65N55
•  44A10

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