A COMPARISON OF DIFFERENT VERSIONS OF THE METHOD OF MULTIPLE SCALES FOR PARTIAL DIFFERENTIAL EQUATIONS

✍ Scribed by H. Boyaci; M. Pakdemirli

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 214 KB
• Volume: 204
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.0951

✦ Synopsis

Applications of the methods of multiple scales (a perturbation method) to partial differential systems arising in non-linear vibrations of continuous systems are considered. Two different versions of the method of multiple scales are applied to two general non-linear models. In one of the models, the small parameter (o) multiplies an arbitrary non-linear cubic operator whereas in the other model, arbitrary quadratic and cubic non-linearities exist. The linear parts of both models are represented by arbitrary operators. General solutions are found by applying different versions of the method of multiple scales. Results of the first version (reconstitution method) and the second version (proposed by Rahman and Burton [8]) are compared for both models. From the comparisons of both methods, it is found that the second version yields better results. Applications of the general models to specific problems are also presented. A final recommendation is to use the second version of the method of multiple scales combined with the direct-perturbation method in finding steady state solutions of partial differential equations.