Towards efficient Runge-Kutta methods for stiff systems
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Order results for mono-implicit Runge-Kutta methods
SIAM Journal on Numerical Analysis
A new type of singly-implicit Runge-Kutta method
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
On a family of cheap symmetric one-step methods of order four
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Journal of Computational and Applied Mathematics
Adaptive ODE solvers in extended Kalman filtering algorithms
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
This paper deals with a special family of implicit Runge-Kutta formulas of orders 2, 4 and 6. These methods are of Gauss type; i.e., they are based on Gauss quadrature formulas of orders 2, 4 and 6, respectively. However, the methods under discussion have only explicit internal stages that lead to cheap practical implementation. Some of the stage values calculated in a step of the numerical integration are of sufficiently high accuracy that allows for dense output of the same order as the Runge-Kutta formula used. On the other hand, the methods developed are A-stable, stiffly accurate and symmetric. Moreover, they are conjugate to a symplectic method up to order 6 at least. All of these make the new methods attractive for solving nonstiff and stiff ordinary differential equations, including Hamiltonian and reversible problems. For adaptivity, different strategies of error estimation are discussed and examined numerically.