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A collocation method for generalized nonlinear Klein-Gordon equation

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Abstract

In this paper, we propose a collocation method for an initial-boundary value problem of the generalized nonlinear Klein-Gordon equation. It possesses the spectral accuracy in both space and time directions. The numerical results indicate the high accuracy and the stability of long-time calculation of suggested algorithm, even for moderate mode in spatial approximation and big time step sizes. The main idea and techniques developed in this work provide an efficient framework for the collocation method of various nonlinear problems.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Ben-Yu Guo & Zhong-Qing Wang

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, People’s Republic of China

    Ben-Yu Guo & Zhong-Qing Wang

  3. Division of Computational Science of E-Institute of Shanghai Universities, Shanghai, 200234, People’s Republic of China

    Ben-Yu Guo & Zhong-Qing Wang

Authors
  1. Ben-Yu Guo
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  2. Zhong-Qing Wang
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Correspondence to Ben-Yu Guo.

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Communicated by: Y. Xu

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Guo, BY., Wang, ZQ. A collocation method for generalized nonlinear Klein-Gordon equation. Adv Comput Math 40, 377–398 (2014). https://doi.org/10.1007/s10444-013-9312-5

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  • DOI: https://doi.org/10.1007/s10444-013-9312-5

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