DIFFERENTIAL TRANSFORM METHOD FOR SOLVING NON-LINEAR DIFFERENTIAL EQUATIONS BY THE ADOMIAN POLYNOMIALS
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2017, Vol 1, Issue 104
Abstract
Purpose. The aim of our study is to consider a novel approach for solving science and engineering problems are described by non-linear ordinary differential equations. Results and originality. The given approach consists in the joint use of the differential transform method and the method of Adomian polynomials. The main idea of proposed method based on solving equations in the image field with approximation of non-linear terms of differential equation by corresponding Adomian polynomials and henceforth obtaining of original of solution as a Taylor series. The proposed approach allows to overcome the mathematical obstacles during differential image calculation of complex non-linearities and essentially reduce the computational cost during searching of approximate solution of non-linear differential equation. Practical value. The proposed approach widens the application of differential transform method to deal with non-linear differential equations with different types of nonlinearity due to the properties and available algorithms of the Adomian polynomials. Numerical experiments demonstrate the application effectiveness of the proposed approach for solving non-linear differential equations and the good agreement with exact solution.
Authors and Affiliations
A. Gusynin
Keywords
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