A NEW MODIFICATION OF THE DIFFERENTIAL TRANSFORM METHOD

In this article, a new modification of the Differential Transform Method, named the ModDTM, is being introduced as a method suitable for solving (1 + 1) partial differential equations, with initial conditions that are specified at the initial value of the spatial variable. Definitions and properties of the method are developed and then applied for solving two nonlinear partial differential equations, namely, the Rosenau-Hyman equation and the Newell-Whitehead-Segel equation, to examine the effectiveness of the method. The solutions obtained are compared with the exact solutions and the solutions by the Reduced Differential Transform Method. It is assessed that the ModDTM is an effective method for solving (1+1) partial differential equations when the attached initial conditions pertain to the spatial variable.