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Hybrid Runge–Kutta methods for ordinary differential equations

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Abstract

We propose a class of s-stage hybrid Runge–Kutta methods for solving ordinary differential equations and study their order conditions and numerical stability property. Examples of second-, third-, and fifth-order hybrid Runge–Kutta methods are given. Numerical experiments are conducted to demonstrate the efficiency of the proposed methods.

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Acknowledgements

The work is partially supported by the National Natural Science Foundation of China under Grant Nos. 11671266 and 11871343.

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Author notes

  1. Zhongli Liu, Jintao Hu & Hongjiong Tian

    Present address: Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai, 200234, China

Authors and Affiliations

  1. School of Statistics and Information, Shanghai University of International Business and Economics, 1900 Wenxiang Road, Shanghai, 201620, China

    Zhongli Liu

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  1. Zhongli Liu
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  2. Jintao Hu
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  3. Hongjiong Tian
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Correspondence to Hongjiong Tian.

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Communicated by Jose Alberto Cuminato.

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Liu, Z., Hu, J. & Tian, H. Hybrid Runge–Kutta methods for ordinary differential equations. Comp. Appl. Math. 39, 176 (2020). https://doi.org/10.1007/s40314-020-01214-7

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  • DOI: https://doi.org/10.1007/s40314-020-01214-7

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