Pakdemirli M.Karahan M.M.F.Boyaci H.2024-07-222024-07-222009http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18520A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. The new method does not violate the main assumption of perturbation series that correction terms should be much smaller than the leading terms. It is proven that for arbitrarily large perturbation parameter values, correction terms remain much smaller that the leading terms. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces much better results for strong nonlinearities.EnglishControl nonlinearitiesConstant amplitudeCorrection termsDamped vibrationsDuffing equationsLeading termsMethod of multiple scaleMultiple scaleNumerical solutionPerturbation parametersPerturbation seriesReal solutionsStrong nonlinearityStrongly nonlinear oscillatorVariable amplitudesAlgorithmsConference paper