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

65M22Solution of discretized equations (IVP of PDE)
35F25Initial value problems for first order nonlinear PDE
35G25Initial value problems for nonlinear higher-order PDE
Full Text: DOI
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