Application of Adomian polynomials for solving nonlinear integro-differential equations

Volume 32, Issue 2, pp 188--200 http://dx.doi.org/10.22436/jmcs.032.02.08

Publication Date: August 29, 2023 Submission Date: May 26, 2023 Revision Date: June 02, 2023 Accteptance Date: July 01, 2023

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Authors

M. A. Abdel-Aty - Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. M. E. Nasr - Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. - Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayat, Saudi Arabia.

Abstract

In this study, the nonlinear integro-differential equation (NIDE) of the second kind is resolved using the Adomian decomposition method (ADM). The term non-linearity can be dealt with easily if used techniques of Adomian polynomials. The existence of at least one positive continuous solution to the nonlinear integro-differential equation is ensured by sufficient conditions. Both the Arzela-Ascoli theorem and the Tychonoff fixed point principle are used in this method. These types of equations are solved using the Adomian decomposition method and the repeated trapezoidal method. The method presented at the end of the article has been tested on many examples and has proven its efficiency after discussing the results.

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Keywords

• Nonlinear integro-differential equation
• Adomian decomposition method
• repeated trapezoidal method
• Tychonoff fixed point theorem
• fixed point theorem

MSC

•  45J05
•  46E15
•  65R20

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