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A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation

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Abstract

In last few years, many ERKN methods have been investigated for solving multi-frequency multidimensional second-order ordinary differential equations, and the numerical efficiency has been checked strongly in scientific computation. But in the constructions of (especially high-order) new ERKN methods, lots of time and effort are costed in presenting the practical order conditions firstly and then in adding some reasonable assumptions to get the coefficient functions finally. In this paper, a feasible and effective technique is given which makes the construction of ERKN methods finished in a few seconds or a few minutes, even for high-order integrators. Moreover, this technique does not need any more information and knowledge except the classical RKN method. And this paper also gives the theoretical explanation to guarantee that the ERKN method obtained from this technique has the same order and the same properties as the underlying RKN method.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, People’s Republic of China

    Hongli Yang

  2. Industrial Center, Nanjing Institute of Technology, Nanjing, People’s Republic of China

    Xianyang Zeng

  3. Department of Mathematics, Nanjing University, Nanjing, People’s Republic of China

    Hongli Yang & Xianyang Zeng

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  1. Hongli Yang
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  2. Xianyang Zeng
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Correspondence to Hongli Yang.

Additional information

The research was supported in part by the Science Foundations of the Nanjing Institute of Technology under Grant CKJA201410 and under Grant QKJA201404, by the Educational Reform Foundations of the Nanjing Institute of Technology under Grant JG201440, by the Natural Science Foundation of China under Grant 11671200.

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Yang, H., Zeng, X. A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation. Numer Algor 76, 761–782 (2017). https://doi.org/10.1007/s11075-017-0281-5

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