Explicit high order methods for the numerical integration of periodic initial-value problems

Two explicit two-step hybrid methods of order 7 and 8 for the numerical integration of second order periodic initial-value problems are developed in this paper. The first of them has a large interval of periodicity and the other a minimal phase-lag. Each of them has seven stages per iteration. Numerical and theoretical results obtained for several well-known problems show the efficiency of the new methods.

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