Interpolants for Runge-Kutta formulas
ACM Transactions on Mathematical Software (TOMS)
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
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
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
On the Preservation of Invariants by Explicit Runge--Kutta Methods
SIAM Journal on Scientific Computing
Structure preservation of exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
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Two new embedded pairs of exponentially fitted explicit Runge-Kutta methods with four and five stages for the numerical integration of initial value problems with oscillatory or periodic solutions are developed. In these methods, for a given fixed @w the coefficients of the formulae of the pair are selected so that they integrate exactly systems with solutions in the linear space generated by {sinh(@wt),cosh(@wt)}, the estimate of the local error behaves as O(h^4) and the high-order formula has fourth-order accuracy when the stepsize h-0. These new pairs are compared with another one proposed by Franco [J.M. Franco, An embedded pair of exponentially fitted explicit Runge-Kutta methods, J. Comput. Appl. Math. 149 (2002) 407-414] on several problems to test the efficiency of the new methods.