Two-dimensional differential transform for partial differential equations. (English) Zbl 1024.65093

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.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05 Heat equation
35L05 Wave equation
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35L60 First-order nonlinear hyperbolic equations
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