CONVERGENCE AND APPLICATION OF A MODIFIED DOUBLE LAPLACE TRANSFORM (MDLT) IN SOME EQUATIONS OF MATHEMATICAL PHYSICS

Tarig M. Elzaki; Mourad Chamekh; Shams A. Ahmed

Tarig M. Elzaki Mathematics Department, College of Sciences and Arts, Alkamel University of Jeddah, Saudi Arabia
Mourad Chamekh Mathematics Department, College of Sciences and Arts, Alkamel University of Jeddah, Saudi Arabi; National Engineering School at Tunis, University of Tunis EI Manar, Lamsin, 1002, Tunis Tunisia
Shams A. Ahmed Department of Mathematics, Faculty of Sciences and Arts, Jouf University, Tubarjal, Saudi Arabia; Department of Mathematics, University of Gezira, Sudan

Article ID: 2409

Keywords: modified double Laplace transform (MDLT); convergence; pseudo-hyperbolic equation; Benney-Luke equation

Abstract

Dealing with a modified double Laplace transform (MDLT) technique, we have established some convergence results. Then, using this new technique, we propose resolutions of some equations such as pseudo-hyperbolic and the Benney-Luke equations. The advantage of MDLT is that we can obtain exact solutions in one step. The technique aims to provide viable results with respect to particular cases. Finally, some numerical results are presented.

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