Revised reduced differential transform method using Adomian's polynomials with convergence analysis

Abstract

The main objective of our analysis is to modify the reduced differential transform method (RDTM) to be applicable for a wide range of nonlinear partial differential equations. The Adomian polynomials are employed to overcome the huge size and complexity of computing reduced differential transforms, and new generalizations of transformed formulas are established. Our new approach provides a series solution with effortless components to compute. A new sufficiency convergence proof of series solution is introduced. The ($1+m$)-dimensional telegraph and Burgers equations are tested to illustrate robustness and reliability of our modification.