Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
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
Optimized Runge-Kutta pairs for problems with oscillating solutions
Journal of Computational and Applied Mathematics
Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods
Numerische Mathematik
Runge-Kutta methods adapted to the numerical integration of oscillatory problems
Applied Numerical Mathematics
Composition Methods for Differential Equations with Processing
SIAM Journal on Scientific Computing
Structure preservation of exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
Trigonometrically-fitted ARKN methods for perturbed oscillators
Applied Numerical Mathematics
Higher-Order Averaging, Formal Series and Numerical Integration I: B-series
Foundations of Computational Mathematics
Heterogeneous Multiscale Methods for Mechanical Systems with Vibrations
SIAM Journal on Scientific Computing
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The stroboscopic averaging method (SAM) is a technique for the integration of highly oscillatory differential systems dy/dt=f(y,t) with a single high frequency. The method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging which constructs an averaged differential system dY/dt=F(Y) whose solutions Y interpolate the sought highly oscillatory solutions y. SAM integrates numerically the averaged system without using the analytic expression of F; all information on F required by the algorithm is gathered on the fly by numerically integrating the originally given system in small time windows. SAM may be easily implemented in combination with standard software and may be applied with variable step-sizes. Furthermore it may also be used successfully to integrate oscillatory DAEs. The paper provides an analytic and experimental study of SAM and two related techniques: the LIPS algorithm of Kirchgraber and multirevolution methods. An error analysis is provided that indicates that the efficiency of all these techniques increases even further when combined with splitting integrators.