Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations

Abstract

In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations $q^{\prime \prime }(t)+Mq(t)=f(q(t))$. The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of $\norm{M}$, which is very crucial for solving oscillatory systems. A fourth-order scheme of the methods is presented. Numerical experiments are implemented to show the remarkable efficiency of the methods proposed in this paper.

References in corpus (1)

• A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs

Cited by in corpus (10)

• On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems
• Functionally-fitted energy-preserving integrators for Poisson systems
• Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations
• Long-term analysis of exponential integrators for highly oscillatory conservative systems
• Long-term analysis of symplectic or symmetric extended RKN methods for nonlinear wave equations
• Long-time analysis of extended RKN integrators for Hamiltonian systems with a solution-dependent high frequency
• Efficient energy-preserving methods for charged-particle dynamics
• Arbitrary-order functionally fitted energy-diminishing methods for gradient systems
• Long-time energy analysis of extended RKN integrators for muti-frequency highly oscillatory Hamiltonian systems
• Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field