Hybrid Numerical-Analytical Approach for Linear and Nonlinear Elliptic Partial Differential Equations Based on the Two-Dimensional Differential Transformation Method

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In this paper, we study the ability of obtaining approximate analytical solutions corresponding to initial value problems associated with linear and nonlinear elliptic partial differential equations, by proposing the two-dimensional differential transformation method (DTM). The approximate solutions for these equations have the form of convergent power series. The tiny relative error occurs after few numbers of iterations shows that, the proposed technique is simple and convenient, revealing the efficiency and the high performance in reducing the size of computational work through obtaining the results.
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Differential Transform Method; Elliptic Partial Differential Equation; Series Solution; Numerical Solution; Closed Form Solution

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