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Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems

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Abstract

In this work, we will propose and analyse a novel reproducing kernel function-based piecewise approach for solving oscillatory systems of second-order initial value problems (IVPs). Also, the approach can be used to effectively solve wave equations with oscillatory solutions via the space semi-discretisation strategy. Five numerical experiments are implemented to illustrate the remarkable accuracy and efficiency of the present approach.

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Acknowledgements

This research was financially supported by the National Natural Science Foundation of China (NSFC) under Grant 11201041 and 11671200, and China Postdoctoral Science Foundation under Grant 2019M651765.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou, 215500, Jiangsu, China

    Fazhan Geng

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu, China

    Fazhan Geng & Xinyuan Wu

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  1. Fazhan Geng
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  2. Xinyuan Wu
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Correspondence to Fazhan Geng.

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Geng, F., Wu, X. Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems. Calcolo 60, 20 (2023). https://doi.org/10.1007/s10092-023-00516-6

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  • DOI: https://doi.org/10.1007/s10092-023-00516-6

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