Abstract
We present an alternative approach proposed by Albrecht to derive general order conditions for Runge-Kutta-Nyström methods and relate it to the classical RKN-theory. The RKN-methods are treated as composite linear methods to yield the general order conditions as orthogonal relations. We then exploit the orthogonal structure of the order conditions and obtain a simple recursion to generate the order conditions. Implications of this approach on the classical RKN-theory are discussed and it may be worthwhile to generalize the approach to other discretizations.
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Funding
The work of the corresponding is supported in part by the National Natural Science Foundation of China under Grant Nos. 11671266 and 11871343, Science and Technology Innovation Plan of Shanghai under Grant No. 20JC1414200, and E-Institutes of Shanghai Municipal Education Commission under Grant No. E03004.
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Communicated by: Long Chen
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Sun, X., Liu, Z. & Tian, H. An alternative approach for order conditions of Runge-Kutta-Nyström methods. Adv Comput Math 47, 70 (2021). https://doi.org/10.1007/s10444-021-09894-3
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DOI: https://doi.org/10.1007/s10444-021-09894-3