Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations. I

DOI10.1007/s10543-008-0201-0zbMath1167.65040OpenAlexW2112945849MaRDI QIDQ1014894

Marianna Khanamiryan

Publication date: 29 April 2009

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-008-0201-0

zbMATH Keywords

numerical examplesasymptotic methodsquadrature methodswaveform relaxation methodshighly oscillatory integralsFilon quadraturelinear and nonlinear systemsHighly oscillatory \(ODE\)s

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Linear ordinary differential equations and systems (34A30) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical quadrature and cubature formulas (65D32) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (13)

Efficient energy-preserving methods for general nonlinear oscillatory Hamiltonian system ⋮ A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems ⋮ Improved filon-type asymptotic methods for highly oscillatory differential equations with multiple time scales ⋮ Adiabatic Filon-type methods for highly oscillatory second-order ordinary differential equations ⋮ Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations ⋮ Quadrature methods for highly oscillatory linear and non-linear systems of ordinary differential equations. II ⋮ Simply improved averaging for coupled oscillators and weakly nonlinear waves ⋮ Symmetric and symplectic exponential integrators for nonlinear Hamiltonian systems ⋮ Asymptotic-numerical solvers for highly oscillatory second-order differential equations ⋮ On highly oscillatory problems arising in electronic engineering ⋮ Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations. I ⋮ Asymptotic-numerical solvers for highly oscillatory ordinary differential equations and Hamiltonian systems ⋮ Parareal Multiscale Methods for Highly Oscillatory Dynamical Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of a collocation method for integrating rapidly oscillatory functions
• On parallel methods for boundary value ODEs
• Artificial time integration
• Remarks on Picard-Lindelöf iteration. II
• Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations. I
• Multi-grid dynamic iteration for parabolic equations
• Remarks on Picard-Lindelöf iteration
• Pseudospectra of wave from relaxation operators
• Numerical approximation of vector-valued highly oscillatory integrals
• Asymptotic Approximations of Integrals
• Convergence of Dynamic Iteration Methods for Initial Value Problems
• On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation
• On SOR Waveform Relaxation Methods
• Efficient quadrature of highly oscillatory integrals using derivatives
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• Error analysis of exponential integrators for oscillatory second-order differential equations
• A Modification of Filon's Method of Numerical Integration

This page was built for publication: Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations. I