APPLICATIONS OF SUMUDU TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

Abstract

In this research solutions of partial differential equations are obtained by using Sumudu transform. The research covers vitally important areas regarding Sumudu transform with details. Chapter one defines Sumudu transform, finds out Sumudu transform for some special functions. Shows the relation between Sumudu transform and Laplace Transform as well as proves some important theorems that widely used Laplace transform. Chapter two introduces Sumudu transform for partial derivatives in order to be used later in solving partial differential equations. Some examples of boundary value problems also covered in this chapter. Chapter three solutions of linear PDEs with constant coefficients is obtained by applying Sumudu transform to them. In chapter four Sumudu transform is applied to Newton problem in fluid dynamics. From the above summary of chapter organization it is easi to conclude that Sumudu transform can be regarded a competitor of Laplace transform in solving differential equations.