Abstract
Problem statement: In this study, a continuous solution for Genesio system was considered using Differential Transformation Method (DTM). Approach: Numerical results were compared to those obtained by the Runge-Kutta method to evaluate the performance of the suggested method. Results: The accuracy of the DTM was tested as the chaotic Genesio system. Conclusion/Recommendations: It was shown that the DTM was robust, accurate and easy to apply and gave analytical solution on each subinterval, which was not possible in the purely numerical method.
Highlights
Differential equations have been the focus of many studies due to their frequent appearance in various applications in fluid mechanics, viscoelasticity, biology, physics and engineering
Much attention has been devoted to the newly developed methods to construct an analytic solutions of nonlinear equation, such methods include the Adomian decomposition method[2,3,5,6] and the Variational Iteration Method (VIM)[6,7,8], the homotopy analysis method and the homotopy-perturbation method[9] and homotopy analysis method[9,10,11]
The given differential equation and related initial conditions are transformed into a recurrence equation that leads to the solution of a system of algebraic equations as coefficients of a power series solution
Summary
Differential equations have been the focus of many studies due to their frequent appearance in various applications in fluid mechanics, viscoelasticity, biology, physics and engineering. Much attention has been devoted to the newly developed methods to construct an analytic solutions of nonlinear equation, such methods include the Adomian decomposition method[2,3,5,6] and the Variational Iteration Method (VIM)[6,7,8], the homotopy analysis method and the homotopy-perturbation method[9] and homotopy analysis method[9,10,11]. The concept of the Differential Transformation Method (DTM) has been introduced to solve linear and nonlinear initial value problems in electric circuit analysis[1].
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