A new algorithm for computing the differential transform in nonlinear two-dimensional partial differential equations

Abstract In this work, a new algorithm is proposed for computing the differential transform of two-dimensional nonlinear functions. This algorithm overcomes the drawbacks of previous algorithms as it is straightforward for any form of analytic nonlinearities and does not require any intermediate calculations or algebraic manipulations. This is accomplished by defining a new form for two dimensional polynomials that generalize the differential transform of the corresponding one-dimensional function to higher dimensions. The correctness of this algorithm is proved via the multivariable Faa di Bruno formula. Several examples with different types of nonlinearities are solved to verify the efficiency of the proposed algorithm.