Solution of Differential Equations by Perturbation Technique Using any Time Transformation
نویسندگان
چکیده
A perturbation algorithm using any time transformation is introduced. To account for the nonlinear dependence of the function, we exhibit the function f of the system in the differential equation. To this end, we introduce the transformation t t w f Te ) , ( , where f is a function that depends on t or w. The problems are solved with new time transformation: Linear damped vibration equation, classical Duffing equation and damped cubic nonlinear equation. Results of Multiple Scales, Lindstedt Poincare method, new method and numerical solutions are contrasted [1-6]. Solution of Differential equations by perturbation technique using any time transformation. In Direct Perturbation Method, mostly secular terms appear of higher orders of the expansion invalidating the solution. In order the avoid this problem a new time transformation has been proposed in our study. The new time transformation is defined as, t t w f Te ) , ( (1) Using the chain rule, we transform the derivate accordingly )) , ( 2 ) , ( ( )) , ( ) , ( ( ' ' )) , ( ) , ( ( ' 2 2 2 t w f t t w f u t w f t t w f u dt u d t w f t t w f u dt du
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