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Generalization of the method of full approximation and its applications

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Abstract

This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the generalized method shows that it is effective and straightforward.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University of Technology, Shanghai

    Dai Shi-qiang

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  1. Dai Shi-qiang
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Dedicated to the Tenth Anniversary and One Hundred Numbers of AMM (I)

Project Supported by National Natural Science Foundation of China and Municipal Natural Science Foundation of Shanghai

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Shi-qiang, D. Generalization of the method of full approximation and its applications. Appl Math Mech 12, 255–264 (1991). https://doi.org/10.1007/BF02098055

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  • DOI: https://doi.org/10.1007/BF02098055

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