An explicit sixth-order method with phase-lag of order eight for y″=f(t,y)
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Numerov method maximally adapted to the Schro¨dinger equation
Journal of Computational Physics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Numerical tracking of small deviations from analytically known periodic orbits
Computers in Physics
SIAM Journal on Numerical Analysis
Generalization of the Störmer method for perturbed oscillators without explicit first derivatives
Proceedings of the on Numerical methods for differential equations
A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators
Journal of Computational and Applied Mathematics
Stability of explicit ARKN methods for perturbed oscillators
Journal of Computational and Applied Mathematics
A class of explicit two-step hybrid methods for second-order IVPs
Journal of Computational and Applied Mathematics
New methods for oscillatory systems based on ARKN methods
Applied Numerical Mathematics
Phase-fitted and amplification-fitted two-step hybrid methods for y˝=f(x,y)
Journal of Computational and Applied Mathematics
Adapted Falkner-type methods solving oscillatory second-order differential equations
Numerical Algorithms
Error analysis of explicit TSERKN methods for highly oscillatory systems
Numerical Algorithms
| Hi-index | 7.29 |
Two-step methods specially adapted to the numerical integration of perturbed oscillators are obtained. The formulation of the methods is based on a refinement of classical Taylor expansions due to Scheifele [G. Scheifele, On the numerical integration of perturbed linear oscillating systems, Z. Angew. Math. Phys. 22 (1971) 186-210]. The key property is that those algorithms are able to integrate exactly harmonic oscillators with frequency @w. The methods depend on a parameter @n=@wh, where h is the stepsize. Based on the B2-series theory of Coleman [J.P. Coleman, Order conditions for a class of two-step methods for y^''=f(x,y), IMA J. Numer. Anal. 23 (2003) 197-220] we derive the order conditions of this new type of method. The linear stability and phase properties are examined. The theory is illustrated with some fourth- and fifth-order explicit schemes. Numerical results carried out on an assortment of test problems (such as the integration of the orbital motion of earth satellites) show the relevance of the theory.