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Explicit pseudo two-step exponential Runge–Kutta methods for the numerical integration of first-order differential equations

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Abstract

This paper is devoted to the explicit pseudo two-step exponential Runge–Kutta (EPTSERK) methods for the numerical integration of first-order ordinary differential equations. These methods inherit the structure of explicit pseudo two-step Runge–Kutta methods and explicit exponential Runge–Kutta methods. We analyze the order conditions and the global errors of the new methods. The new methods are of order s + 1 with s-stages for some suitable nodes. Numerical experiments are reported to show the convergence and the efficiency of the new methods.

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Acknowledgments

The authors are very grateful to the editor and anonymous referees for their invaluable comments and suggestions which helped to improve the manuscript.

Funding

This research is partially supported by the National Natural Science Foundation of China (No. 11571302), the Natural Science Foundation of Shandong Province, China (No. ZR2018MA024), the project of Shandong Province higher Educational Science and Technology Program (Nos. J18KA247, J17KA190), and the foundation of innovative science and technology for youth in universities of Shandong Province (2019KJI001).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Yonglei Fang

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Xianfa Hu

  3. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China

    Jiyong Li

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  1. Yonglei Fang
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Correspondence to Yonglei Fang.

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Fang, Y., Hu, X. & Li, J. Explicit pseudo two-step exponential Runge–Kutta methods for the numerical integration of first-order differential equations. Numer Algor 86, 1143–1163 (2021). https://doi.org/10.1007/s11075-020-00927-4

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  • DOI: https://doi.org/10.1007/s11075-020-00927-4

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