Applications of New Double Integral Transform (Laplace–Sumudu Transform) in Mathematical Physics

Shams A Ahmed

doi:10.1155/2021/6625247

Abstract

The primary purpose of this research is to demonstrate an efficient replacement of double transform called the double Laplace–Sumudu transform (DLST) and prove some related theorems of the new double transform. Also, we will discuss the fundamental properties of the double Laplace–Sumudu transform of some basic functions. Then, by utilizing those outcomes, we will apply it to the partial differential equations to show its simplicity, efficiency, and high accuracy.

Highlights

Partial differential equations are used to describe many realworld problems arising in all the fields of applied science and issues associated with engineering
One of the problems with these equations is that they are very difficult to solve equations with unknown functions of two variables sometimes. This problem was solved by combining the Laplace transforms and Sumudu transform to give another double transform which is called the double Laplace–Sumudu transform
The main objective of this paper is to develop new applications of the double Laplace–Sumudu transform for solving linear partial differential equations of the type (1) subject to the initial conditions (2) and boundary conditions (3)

Summary

Introduction

Partial differential equations are used to describe many realworld problems arising in all the fields of applied science and issues associated with engineering. Some researchers have combined these integral transforms with other methods such as the differential transform method, homotophy perturbation method, Adomian decomposition method and variational iteration method [7,8,9,10,11,12,13] for solving many nonlinear differential equations The usefulness of these equations has attracted the attention of many scholars throughout the history of applied sciences. The main objective of this paper is to develop new applications of the double Laplace–Sumudu transform for solving linear partial differential equations of the type (1) subject to the initial conditions (2) and boundary conditions (3). The proposed integral transform is successfully applied to a wide range of linear partial differential equations in mathematical physics

Preliminaries

Fundamental Properties of Double Laplace– Sumudu Transform

Elucidative Examples

Conclusion