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
Diagonally implicit Runge-Kutta-Nystro¨m methods for oscillatory problems
SIAM Journal on Numerical Analysis
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
Runge-Kutta(-Nystro¨m) methods for ODEs with periodic solutions based on trigonometric polynomials
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
A phase-fitted collocation-based Runge-Kutta-Nyström method
Applied Numerical Mathematics
Collocation---Based Two Step Runge---Kutta Methods for Ordinary Differential Equations
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
Two step Runge-Kutta-Nyström methods for oscillatory problems based on mixed polynomials
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Exponentially fitted two-step hybrid methods for y″=f(x,y)
Journal of Computational and Applied Mathematics
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
General linear methods for y˝=f(y(t))
Numerical Algorithms
Exponentially fitted singly diagonally implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
P-stable general Nyström methods for y˝=f(y(t))
Journal of Computational and Applied Mathematics
Order conditions for General Linear Nyström methods
Numerical Algorithms
| Hi-index | 0.00 |
P-stability is an important requirement in the numerical integration of stiff oscillatory systems, but this desirable feature is not possessed by any class of numerical methods for y驴 = f(x, y). It is known, for example, that P-stable linear multistep methods have maximum order two and symmetric one step polynomial collocation methods can't be P-stable (Coleman 1992). In this note we show the existence of P-stable methods within a general class of two step Runge-Kutta-Nystr枚m methods.