A new algorithm for calculating two-dimensional differential transform of nonlinear functions. (English) Zbl 1179.65121

Chang, Shih-Hsiang; Chang, I-Ling

Appl. Math. Comput. 215, No. 7, 2486-2494 (2009).

Summary: A new algorithm for calculating the two-dimensional differential transform of nonlinear functions is developed. This new technique is illustrated by studying suitable forms of nonlinearity. Three strongly nonlinear partial differential equations are then solved by the differential transform method to demonstrate the validity and applicability of the proposed algorithm. The present framework offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability.

MSC:

65M22	Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
35F25	Initial value problems for nonlinear first-order PDEs
35G25	Initial value problems for nonlinear higher-order PDEs

Keywords:

differential transform method; nonlinearity; numerical examples; Goursat problem; initial-value problems; algorithm

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