Solution of Partial Differential Equations via ”Double SEE-Aboodh Transform”

Abstract

In this paper, we introduce a new double integral technique namely “Double SEE-Aboodh
Teachnique” to evaluate the solution of the general linear partial differential equations (LPDE’s). Many basic
functions are used to prove the importance of this double technique. This technique depends on the SEE
(Sadik-Emad-Eman) and Aboodh transforms, where these two transforms are combined to obtain the double
SEE-Aboodh transform. It turns out that been this technique is used; the steps for solving partial differential
equations are easy and simple to obtain the exact solution. Combining two different transformations is aimed
at finding a new technique for finding exact solutions to partial differential equations in a way and manner
that is easier and simpler than previous techniques. Especially after the emergence of many new life problems,
it requires finding simple modern techniques that are easy to use in algebraic calculations, far from difficulty
and complexity, and this is what we found in our paper through the examples for which exact solutions were
found. Through this double transform we obtain many double transforms, the most important of which are
the double Aboodh-Laplace, double Aboodh transforms, and others.