Combined Integral Transform - Adomain Decomposition Methods For Solving Nonlinear Differential Equations

Abstract

The Adomain decomposition method is a semi-analytical technique for solving nonlinear differential equations. In the literature, one can find that this method is combined with integral transforms such as Laplace, Natural, Sumudu, and Elzaki transforms. This thesis presents some famous integral transforms couplied with the Adomain decomposition method. These transforms include, the natural transform, the double natural transform, Laplace transform, the double Laplace transform, Elzaki transform and Sumudu transform. These transforms are presented with their properties. Then they are combined with the Adomain decomposition method to solve nonlinear ordinary and partial differential equations