Analytical Solution of Non-Linear Partial Differential Equations Via the New Double Integral Transform with Combined Iterative Method

Abstract

The analytical solution of nonlinear partial differential equations (NLPDEs) is investigated in this thesis. This is accomplished by the novel application of the Double Laplace Sumudu Transform (DLST) in conjunction with an iterative technique. Obtaining analytical solutions for non-linear partial dif ferential equations continues to be a difficult challenge. In this paper, the DLST-I method is presented, which involves the application of the Double Laplace Sumudu Transform and an iterative approach to the process of de composing nonlinear terminology. In this research, our goal is to improve our comprehension of intricate events and extend the potential of analytical meth ods for non-linear partial differential equations. The potential impact that the proposed technique could have on the domains of science, engineering, and mathematics is the source of the methodology’s significance.