Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Starting algorithms for implicit Runge-Kutta-Nystro¨m methods
Applied Numerical Mathematics
Stage Value Predictors and Efficient Newton Iterations in Implicit Runge--Kutta Methods
SIAM Journal on Scientific Computing
IRK methods for DAE: starting algorithms
Proceedings of the on Numerical methods for differential equations
Are high order variable step equistage initializers better than standard starting algorithms?
Journal of Computational and Applied Mathematics
Stage value predictors for additive and partitioned Runge-Kutta methods
Applied Numerical Mathematics
Stage value predictors for additive and partitioned Runge--Kutta methods
Applied Numerical Mathematics
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When second order differential equations are solved with Runge-Kutta-Nyström methods, the computational effort is dominated by the cost of solving the nonlinear system. That is why it is important to have good starting values to begin the iterations. In this paper we consider a type of starting algorithms without additional computational cost. We study the general order conditions and the maximum order achieved when the Runge-Kutta-Nyström method satisfies some simplifying assumptions.