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A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations

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Abstract

In this paper, a simple approach to enlarging convergence regions of perturbation approximations is proposed. Based on the so-called general Taylor theorems, this approach has a solid mathematical foundation. Moreover, it is rather simple to apply. Two nonlinear equations, the Riccati equation and the Van der Pol equation are used as examples to illustrate the validity and the great potential of this approach.

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Authors and Affiliations

  1. School of Naval Architecture and Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200030, People's Republic of China

    Shi-Jun Liao

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  1. Shi-Jun Liao
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Liao, SJ. A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations. Nonlinear Dynamics 19, 93–111 (1999). https://doi.org/10.1023/A:1008373627897

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