A new theoretical approach to Runge-Kutta methods
SIAM Journal on Numerical Analysis
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
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
Mixed collocation methods for y′′=fx,y
Journal of Computational and Applied Mathematics
Exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Weights of the exponential fitting multistep algorithms for first-order ODEs
Journal of Computational and Applied Mathematics
Frequency determination and step-length control for exponentially-fitted Runge---Kutta methods
Journal of Computational and Applied Mathematics
Frequency evaluation in exponential fitting multistep algorithms for ODEs
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
An embedded pair of exponentially fitted explicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
Exponential fitted Runge--Kutta methods of collocation type: fixed or variable knot points?
Journal of Computational and Applied Mathematics
Exponentially fitted explicit Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
An explicit Numerov-type method for second-order differential equations with oscillating solutions
Computers & Mathematics with Applications
Phase-fitted and amplification-fitted two-step hybrid methods for y˝=f(x,y)
Journal of Computational and Applied Mathematics
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This paper can be seen as a further investigation of the frequency evaluation techniques which are very recently proposed by Ixaru et al. for exponentially fitted multistep algorithms for first-order ordinary differential equations (ODEs). The question answered was how the frequencies should be tuned in order to have a maximal benefit from exponentially fitted methods. In a previous paper, this frequency evaluation algorithm was successfully applied in a direct way to a second-order exponentially fitted Runge-Kutta (EFRK) method of collocation type but such a direct application is impossible for higher-order EFRK methods. To overcome this difficulty we develop an efficient extension of Ixaru's frequency evaluation algorithm for the exponentially fitted RadauIIA method of third order. It is an adaption of Ixaru's algorithm in the sense that instead being applied globally, it is applied stagewise. Numerical experiments illustrate the properties of the developed algorithm.