Abstract
In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential equations with initial boundary value (IBVP). According to boundary condition, the initial condition is expanded into a Fourier series. After that, the IBVP is transformed to an iterative relation in K-domain. The series solution or exact solution can be obtained. The rationality and practicability of the algorithm FDTM are verified by comparisons of the results obtained by FDTM and the existing analytical solutions.
Highlights
The differential transform method (DTM) is a powerful approximate analytic method for solving linear and nonlinear differential equations
The research on solution of the initial boundary value problem of partial differential equation system based on DTM is scarce
The aim of this paper is to extend the differential transformation method to solve partial differential equation system with initial and three typical zero boundary conditions
Summary
The differential transform method (DTM) is a powerful approximate analytic method for solving linear and nonlinear differential equations. There still exist some difficulties in solving system of differential equations with initial and boundary condition(s) by the DTM. The research on solution of the initial boundary value problem of partial differential equation system based on DTM is scarce. The aim of this paper is to extend the differential transformation method to solve partial differential equation system with initial and three typical zero boundary conditions. The method can be used to evaluate the approximating solution by the finite Taylor series and by an iteration procedure described by the transformed equations obtained from the original equation using the operations of differential transformation.
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