Shampine, L. F.; Baca, L. S. Fixed versus variable order Runge-Kutta. (English) Zbl 0594.65047 ACM Trans. Math. Softw. 12, 1-23 (1986). The aim of the paper consists in a comparison of the numerical efficiency of a variable order Runge-Kutta code based on polynomial extrapolation of the midpoint rule to a fixed order Runge-Kutta method consisting of a (7,8) pair with a 13-stage formula of order 8. After an extensive report on numerical experiments with a restricted three body problem the authors arrive at the conclusion that their fixed order method turns out to be more efficient than the best extrapolation procedures. Reviewer: G.Merz Cited in 7 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 70F07 Three-body problems 34A34 Nonlinear ordinary differential equations and systems Keywords:comparison of numerical efficiency; variable order Runge-Kutta code; polynomial extrapolation; fixed order; numerical experiments PDFBibTeX XMLCite \textit{L. F. Shampine} and \textit{L. S. Baca}, ACM Trans. Math. Softw. 12, 1--23 (1986; Zbl 0594.65047) Full Text: DOI Link