Pakdemirli M.Karahan M.M.F.Boyaci H.2024-07-222024-07-2220091300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18970A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed for the first time. 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. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces better results for strong nonlinearities. © Association for Scientific Research.EnglishAll Open Access; Gold Open AccessControl nonlinearitiesNonlinear equationsNumerical methodsConvergence propertiesLindstedt-Poincare methodMethod of multiple scaleMultiple scales methodsNumerical solutionPerturbation methodPerturbation parametersVariable amplitudesPerturbation techniquesArticle10.3390/mca14010031