Symmetric collocation ERKN methods for general second-order oscillators
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For the numerical solution of the general second-order oscillatory system \(y''+ M y = f(y,y')\), You et al. (Numer Algorithm 66:147–176, 2014) proposed the extended Runge–Kutta–Nyström (ERKN) methods. This paper is devoted to symmetric collocation ERKN methods of Gauss and Lobatto IIIA types by Lagrange interpolation. Linear stability of the new ERKN methods is analyzed. Numerical experiments show the high effectiveness of the new ERKN methods compared to their RKN counterparts.
KeywordsExtended Runge–Kutta–Nyström methods Order condition Symmetry condition Second-order oscillator Collocation
Mathematics Subject Classification.Primary 65L05 65L12
The authors are grateful to the anonymous referees for their invaluable comments and constructive suggestions which help greatly to improve the manuscript. This research was partially supported by National Natural Science Foundation of China (Nos. 11171155, 11871268, 11571302), Natural Science Foundation of Jiangsu Province, China (No. BK20171370), Natural Science Foundation of Shandong Province (No. ZR2018MA024), the Foundation of Scientific Research Project of Shandong Universities (Nos. J17KA190, KJ2018BAI031), and the Youth Foundation for Innovative Science and Technology in Universities of Shandong Province, China (No. 2019KJI001).
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