
Two-step Runge-Kutta methods are a generalization of classical one-step methods, where each integration step reuses quantities computed in the previous step. Although they can attain higher accuracy for a given number of function evaluations than for standard Runge-Kutta methods, they are less convenient to implement with variable stepsize. The authors propose to overcome this disadvantage by representing data passed from step to step in Nordsieck representation, that is using scaled derivatives up to the order of the method. This has additional advantages in that new reliable error estimators become available. The estimator is seen to be very accurate on numerical tests and the implementation overall, at least for low order methods in the new family, is seen to be competitive.
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical examples, Nordsieck representation, error estimation, two-step Runge-Kutta methods, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Error bounds for numerical methods for ordinary differential equations
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical examples, Nordsieck representation, error estimation, two-step Runge-Kutta methods, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Error bounds for numerical methods for ordinary differential equations
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