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DIFFERENTIAL TRANSFORMATION METHOD FOR NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

Year 2015, Volume 5, Issue 1, 37 - 50, 12.02.2016

Abstract

This work presents solution of nonlinear differential-difference equations such as the discretized mKdV lattice equation, the discretized nonlinear Schrödinger equation and the Toda Lattice equation by Differential Transformation Method (DTM). This method provides more realistic solutions by solving the nonlinear differential equations without any simplification and the series solutions which generally converge very rapidly in real physical models. Moreover, no linearization or perturbation is required in this method. By using this method, exact solutions may be obtained without any need of cumbersome work. This method is a useful tool for analytical and numeric solutions. The results of the present method are compared with those obtained by Adomian Decomposition Method and exact solutions. The results have shown that DTM method has better performs. 

DIFFERENTIAL TRANSFORMATION METHOD FOR NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

Year 2015, Volume 5, Issue 1, 37 - 50, 12.02.2016

Abstract

This work presents solution of nonlinear differential-difference equations such as the discretized mKdV lattice equation, the discretized nonlinear Schrödinger equation and the Toda Lattice equation by Differential Transformation Method (DTM). This method provides more realistic solutions by solving the nonlinear differential equations without any simplification and the series solutions which generally converge very rapidly in real physical models. Moreover, no linearization or perturbation is required in this method. By using this method, exact solutions may be obtained without any need of cumbersome work. This method is a useful tool for analytical and numeric solutions. The results of the present method are compared with those obtained by Adomian Decomposition Method and exact solutions. The results have shown that DTM method has better performs.

Details

Primary Language English
Subjects Engineering
Journal Section Review Articles
Authors

İbrahim ÇELİK


Duygu ESKİN This is me

Publication Date February 12, 2016
Published in Issue Year 2015, Volume 5, Issue 1

Cite

APA Çelik, İ. & Eskin, D. (2016). DIFFERENTIAL TRANSFORMATION METHOD FOR NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS . Ordu Üniversitesi Bilim ve Teknoloji Dergisi , 5 (1) , 37-50 . Retrieved from https://dergipark.org.tr/en/pub/ordubtd/issue/11069/132194