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A new embedded pair of Runge-Kutta formulas of orders 5 and 6. (English) Zbl 0712.65070
Authors’ summary: A new pair of embedded Runge-Kutta (RK) formulas of orders 5 and 6 is presented. It is derived from a family of RK methods depending on eight parameters by using certain measures of accuracy and stability. Numerical tests comparing its efficiency to other formulas of the same in current use are presented. With an extra function evaluation per step, a \(C^ 1\)-continuous interpolant of order 5 can be obtained.
Reviewer: I.Dvořák

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
Full Text: DOI
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