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Flexible exponential integration methods for large systems of differential equations

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Abstract

In this paper, we describe a flexible variant of exponential integration methods for large systems of differential equations. This version possesses the flexibility and generality which allows to further exploit the special structure of the system. By using modified B-series and bi-coloured rooted trees, we can derive the general structure of the classical order conditions for these schemes. Some numerical schemes are constructed and the order conditions are derived. Numerical experiments with reaction-diffusion type problems are included.

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Acknowledgments

The authors gratefully acknowledge the supports of the National Science Foundation Grant (11471217) of China.

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Authors and Affiliations

  1. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Dongping Li, Yuhao Cong & Kaifeng Xia

  2. Department of Mathematics, Changchun Normal University, Changchun, 130032, People’s Republic of China

    Dongping Li

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  1. Dongping Li
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  2. Yuhao Cong
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  3. Kaifeng Xia
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Correspondence to Yuhao Cong.

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Li, D., Cong, Y. & Xia, K. Flexible exponential integration methods for large systems of differential equations. J. Appl. Math. Comput. 51, 545–567 (2016). https://doi.org/10.1007/s12190-015-0919-1

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  • DOI: https://doi.org/10.1007/s12190-015-0919-1

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