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Zbl 1024.65093
Jang, Ming-Jyi; Chen, Chieh-Li; Liu, Yung-Chin
Two-dimensional differential transform for partial differential equations. (English)
[J] Appl. Math. Comput. 121, No.2-3, 261-270 (2001). ISSN 0096-3003

Summary: The differential transform is a numerical method for solving differential equations. In this paper, we present the definition and operation of the two-dimensional differential transform. A distinctive feature of the differential transform is its ability to solve linear and nonlinear differential equations. Partial differential equations of parabolic, hyperbolic, elliptic and nonlinear types can be solved by the differential transform. We demonstrate that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35J05 Laplace equation, etc.
35K05 Heat equation
35L05 Wave equation
35A22 Transform methods (PDE)
35L60 First-order nonlinear hyperbolic equations

Keywords: Poisson equation; wave equation; heat equation; nonlinear first-order hyperbolic equation; numerical examples; initial value problem; differential transform; nonlinear partial differential equation

Cited in: Zbl 1237.35150

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Zentralblatt MATH Berlin [Germany]