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A new family of A-stable Runge-Kutta methods with equation-dependent coefficients for stiff problems

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Abstract

A new family of A-stable Runge-Kutta methods with equation-dependent (EDRK) coefficients for the numerical solution of stiff differential equations is investigated. The newly constructed four-stage EDRK methods are of algebraic order five. The linear stability properties are analyzed. Numerical experiments are carried out to show the efficiency of the new methods compared with the existing codes in the literature.

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Acknowledgements

The authors are deeply grateful to the anonymous referees, for their careful reading of the manuscript, pointing out the mistakes and, as the experts in the field, giving the valuable comments and suggestions.

Funding

This research is partially supported by the National Natural Science Foundation of China (Nos. 11571302, 11871268, 11171155), the Natural Science Foundation of Shandong Province, China (No. ZR2018MA024), the Natural Science Foundation of Jiangsu Province, China (No. BK20171370), and the project of Shandong Province higher Educational Science and Technology Program (Nos. KJ2018BAI031, J17KA190).

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Authors and Affiliations

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

    Yonglei Fang & Yanping Yang

  2. College of Sciences, Nanjing Agricultural University, Nanjing, 210095, People’s Republic of China

    Xiong You

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Bin Wang

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  1. Yonglei Fang
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  2. Yanping Yang
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  3. Xiong You
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  4. Bin Wang
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Correspondence to Yonglei Fang.

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Fang, Y., Yang, Y., You, X. et al. A new family of A-stable Runge-Kutta methods with equation-dependent coefficients for stiff problems. Numer Algor 81, 1235–1251 (2019). https://doi.org/10.1007/s11075-018-0619-7

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  • DOI: https://doi.org/10.1007/s11075-018-0619-7

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