In this article, as a method suitable for solving (1 + 1) partial differential equations, a new modification of the Differential Transform Method, called the ModDTM, is implemented with initial conditions which are defined at the initial value of the spatial variable. The method's concepts and properties are developed and then applied to test the efficacy of the method in order to solve two nonlinear partial differential equations, namely the Rosenau-Hyman equation and the Newell-Whitehead-Segel equation. The solutions obtained are compared via the Reduced Differential Transform Method with the exact solutions and the solutions. It is assessed that when the attached initial conditions apply to the spatial variable, ModDTM is an efficient tool for solving (1+1) partial differential equations.
Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/5475
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