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Math. Comput. Appl. 1999, 4(3), 273-282; doi:10.3390/mca4030273

A Comparison of Different Versions of the Method of Multiple Scales for an Arbitrary Model of Odd Nonlinearities

Department of Mechanical Engineering, Celal Bayar University 45140, Muradiye, Manisa, Turkey
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Published: 1 December 1999
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Abstract

A general model of cubic and fifth order nonlinearities is considered. The linear part as well as the nonlinearities are expressed in terms of arbitrary operators. Two different versions of the method of multiple scales are used in constructing the general transient and steady-state solutions of the model: Modified Rahman-Burton method and the Reconstitution method. It is found that the usual ordering of reconstitution can be used, if at higher orders of approximation, the time scale corresponding to that order is considered and all other time derivatives are ignored. Results are applied to an example and steady-state solutions are compared numerically for both methods.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Pakdemirli, M.; Boyacı, H. A Comparison of Different Versions of the Method of Multiple Scales for an Arbitrary Model of Odd Nonlinearities. Math. Comput. Appl. 1999, 4, 273-282.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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