Embedded pseudo-Runge-Kutta methods
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
Stability of parallel explicit ODE methods
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
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
Continuous variable stepsize explicit pseudo two-step RK methods
Journal of Computational and Applied Mathematics
Mixed collocation methods for y′′=fx,y
Journal of Computational and Applied Mathematics
An embedded pair of exponentially fitted explicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
Trigonometrically fitted predictor: corrector methods for IVPs with oscillating solutions
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Exponentially fitted explicit Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
Analysis of trigonometric implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
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Explicit pseudo two-step Runge-Kutta (EPTRK) methods belong to the wider class of general linear multistep methods. The particularity of EPTRK methods is that they do not use the last two iterates as conventional two-step methods do. Rather, they predict the intermediate stage values and combine them with the last iterate to obtain the next iterate. EPTRK methods were initially designed to suit parallel computers, but they have been shown to achieve arbitrary high-order and thus can be useful as conventional explicit RK methods on sequential computers as well. Our contribution in this paper is to present a new family of functionally fitted EPTRK methods aimed at integrating an equation exactly if its solution is a linear combination of a chosen set of basis functions. We use a variation of collocation techniques to show that this new family, which we call FEPTRK, shares the same accuracy properties as EPTRK. The added advantage is that FEPTRK can use specific fitting functions to capitalize on the special properties of the problem that may be known in advance.