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Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method

Author name : Shams Eldeen Ahmed Abdelmajed Mohammed
Publication Date : 2022-05-25
Journal Name : Axioms

Abstract

This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs.

Keywords

double Laplace–Sumudu transform; single Laplace transform; single Sumudu transform; new iterative method; nonlinear partial differential equations

Publication Link

https://doi.org/10.3390/axioms11060247

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