New Approach to Laplace Differential Transform Method to Solve Nonlinear Partial Differential Equations
Musilimu Taiwo, Gabriel, O. Olupitan and Kehinde, F. Adedapo
Keywords: Generalized Drinfeld-Sokolov equations, Kaup-Kupershmidt equation, Laplace Differential Transform Method, Nonlinear Partial differential equations.
Abstract
In this article, we develop a scheme for the Laplace differential transform method (LDTM) to obtain approximate analytical solutions in form of a series of mathematical models of nonlinear partial differential equations. The technique is based on the application of the Laplace transform to nonlinear partial differential equations. The nonlinear term can be handled with the help of the differential transform method. We applied this method to two types of nonlinear Partial differential equations, namely the-Kaup-Kupershmidt equation and generalized DrinfeldSokolov equations. The results obtained were compared with exact solutions, which revealed that LDTM is efficient, accurate, reliable and also applicable for solving many other nonlinear Partial differential equations.