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Contractivity-preserving explicit Hermite-Obrechkoff ODE solver of order 13. (English) Zbl 1284.65087

Summary: A new optimal, explicit, Hermite-Obrechkoff method of order 13, denoted by HO(13), that is contractivity-preserving (CP) and has nonnegative coefficients is constructed for solving nonstiff first-order initial value problems. Based on the CP conditions, the new 9-derivative HO(13) has maximum order 13. The new method usually requires significantly fewer function evaluations and significantly less CPU time than the Taylor method of order 13 and the Runge-Kutta method DP(8,7)13M to achieve the same global error when solving standard \(N\)-body problems.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
70F10 \(n\)-body problems

Software:

STDTST; NSDTST
PDFBibTeX XMLCite
Full Text: DOI

References:

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