A Study of Solutions for Some Classes of PDEs Arising in Physics and Engineering Using Modified Reduced Differential Transform Method

This paper successfully employs a combined methodology that integrates the reduced differential transform approach, Laplace transform, and Padé approximants to solve diverse partial differential equations with real and complex variables. The proposed method, known as the modified reduced differential transform method (MRDTM), extends the interval of convergence with less computing time. An interesting aspect of this method is its capability to produce an analytic exact solution with only a few computable terms. The paper provides practical applications through notable examples encompassing the Klein–Gordon equation, the Schrödinger equation, the nonlinear reaction–diffusion–convection equation, and systems of linear and nonlinear PDEs. Primary results on certain test problems demonstrate the efficiency and ability of the method in solving diverse classes of partial differential equations, and therefore, it can be used as an alternative for dealing with such problems that do not have analytic solutions.