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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.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35K05Heat equation
35L05Wave equation (hyperbolic PDE)
35A22Transform methods (PDE)
35L60Nonlinear first-order hyperbolic equations