Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Exponential fitted Runge--Kutta methods of collocation type: fixed or variable knot points?
Journal of Computational and Applied Mathematics
Runge-Kutta methods adapted to the numerical integration of oscillatory problems
Applied Numerical Mathematics
Structure preservation of exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type
Journal of Computational and Applied Mathematics
Correction of eigenvalues estimated by the Legendre---Gauss Tau method
Numerical Algorithms
Exponentially fitted singly diagonally implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
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The construction of symmetric and symplectic exponentially-fitted Runge---Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions deserves a lot of interest. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators of eighth-order are studied and constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (2004). Numerical experiments for some oscillatory problems are presented.