Summary
Recently there has been considerable interest in the approximate numerical integration of the special initial value problemy″=f(x, y) for cases where it is known in advance that the required solution is periodic. The well known class of Störmer-Cowell methods with stepnumber greater than 2 exhibit orbital instability and so are often unsuitable for the integration of such problems. An appropriate stability requirement for the numerical integration of periodic problems is that ofP-stability. However Lambert and Watson have shown that aP-stable linear multistep method cannot have an order of accuracy greater than 2. In the present paper a class of 2-step methods of Runge-Kutta type is discussed for the numerical solution of periodic initial value problems.P-stable formulae with orders up to 6 are derived and these are shown to compare favourably with existing methods.
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Cash, J.R. High orderP-stable formulae for the numerical integration of periodic initial value problems. Numer. Math. 37, 355–370 (1981). https://doi.org/10.1007/BF01400315
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DOI: https://doi.org/10.1007/BF01400315