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Compact ETDRK scheme for nonlinear dispersive wave equations

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Abstract

In this paper, a fourth-order scheme is presented for nonlinear dispersive wave equations. The scheme uses the fourth-order compact finite-difference method for discretization in space and the fourth-order exponential time-differencing Runge–Kutta (ETDRK) method for the temporal direction, respectively. The Cauchy integral formula takes effect on stabilizing the fourth-order ETDRK method, and deals with nondiagonal large sparse coefficient matrix which has complex eigenvalues tend to zero. It can be observed by numerical experiments that the numerical method is performed efficiently for the solitary wave profile of the Rosenau–KdV–RLW equation.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China

    Muyassar Ahmat

  2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China

    Jianxian Qiu

Authors
  1. Muyassar Ahmat
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  2. Jianxian Qiu
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Correspondence to Jianxian Qiu.

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Communicated by Abdellah Hadjadj.

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The research is partly supported by NSFC Grant 12071392.

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Ahmat, M., Qiu, J. Compact ETDRK scheme for nonlinear dispersive wave equations. Comp. Appl. Math. 40, 286 (2021). https://doi.org/10.1007/s40314-021-01687-0

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  • DOI: https://doi.org/10.1007/s40314-021-01687-0

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