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Derivation of efficient, continuous, explicit Runge-Kutta methods. (English) Zbl 0760.65073
This paper deals with continuously differentiable, explicit Runge-Kutta methods. Special formulas with minimal number of stages and minimal truncation error or maximal stability region are deduced. Numerical results and comparisons with known formulas are given.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
Software:
NSDTST; STDTST
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