Natural continuous extensions of Runge-Kutta formulas
Mathematics of Computation
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
SIAM Journal on Numerical Analysis
Derivation of efficient, continuous, explicit Runge-Kutta methods
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The tolerance proportionality of adaptive ODE solvers
Journal of Computational and Applied Mathematics - Special issue on numerical methods for ordinary differential equations
A general class of two-step Runge-Kutta methods for ordinary differential equations
SIAM Journal on Numerical Analysis
Implementation of two-step Runge-Kutta methods for ordinary differential equations
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Order conditions for two-step Runge-Kutta methods
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Order Conditions for General Two-Step Runge--Kutta Methods
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pseudo-Runge-Kutta Methods Involving Two Points
Journal of the ACM (JACM)
Construction of two-step Runge--Kutta methods with large regions of absolute stability
Journal of Computational and Applied Mathematics
Derivation of continuous explicit two-step Runge-Kutta methods of order three
Journal of Computational and Applied Mathematics
Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations
Journal of Computational and Applied Mathematics
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We describe a new representation of explicit two-step Runge-Kutta methods for ordinary differential equations. This representation makes it possible for the accurate and reliable estimation of local discretization error and facilitates the efficient implementation of these methods in a variable stepsize environment.