Journal of Computational and Applied Mathematics
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
High-order P-stable multistep methods
Journal of Computational and Applied Mathematics
A Numerov-type method for the numerical solution of the radial Schro¨dinger equation
Applied Numerical Mathematics
Mixed collocation methods for y′′=fx,y
Journal of Computational and Applied Mathematics
A phase-fitted collocation-based Runge-Kutta-Nyström method
Applied Numerical Mathematics
A class of explicit two-step hybrid methods for second-order IVPs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Frequency evaluation for exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
Stability regions of one step mixed collocation methods for y" = f (x, y)
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Scheifele two-step methods for perturbed oscillators
Journal of Computational and Applied Mathematics
On Numerov's method for a class of strongly nonlinear two-point boundary value problems
Applied Numerical Mathematics
Mathematics and Computers in Simulation
Exponentially fitted two-step hybrid methods for y″=f(x,y)
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
This paper provides a theoretical framework for a new type of phase-fitted and amplification-fitted two-step hybrid (FTSH) methods which is introduced by the author in [H. Van de Vyver, A phase-fitted and amplification-fitted explicit two-step hybrid method for second-order periodic initial value problems, Internat. J. Modern Phys. C 17 (2006) 663-675]. The methods constitute a modification of dissipative two-step hybrid methods in the sense that two free parameters are added to eliminate the phase-lag and the amplification error. The methods are useful only when a good estimate of the frequency of the problem is known in advance. The parameters depend on the product of the estimated frequency and the stepsize. The algebraic order, zero-stability, stability and phase properties are examined. The theory is illustrated with sixth-order explicit FTSH methods. Numerical results carried out on an assortment of test problems show the relevance of the theory.