A New Perturbation Algorithm With Better Convergence Properties: Multiple Scales Lindstedt Poincare Method

Pakdemirli, M.; Karahan, M. M. F.; Boyacı, H.

doi:10.3390/mca14010031

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Article

1 April 2009

14 Pages

A New Perturbation Algorithm With Better Convergence Properties: Multiple Scales Lindstedt Poincare Method

and

Department of Mechanical Engineering Celal Bayar University, Muradiye 45140 Manisa, Turkey

Author to whom correspondence should be addressed.

Math. Comput. Appl.2009, 14(1), 31-44;https://doi.org/10.3390/mca14010031

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Abstract

A 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.

Keywords:

Perturbation Methods; Lindstedt Poincare method; Multiple Scales method; Numerical Solutions

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