Asymptotic-numerical solvers for highly oscillatory second-order differential equations

DOI10.1016/j.apnum.2018.11.004zbMath1410.34057OpenAlexW2901842440MaRDI QIDQ1728340

Zhongli Liu, Tianhai Tian, Hong-Jiong Tian

Publication date: 22 February 2019

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.11.004

zbMATH Keywords

asymptotic expansionsecond-order ordinary differential equationmultiple time scalesmodulated Fourier expansionhighly oscillatory problem

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Multiple scale methods for ordinary differential equations (34E13)

Related Items (4)

Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems ⋮ Solving second-order telegraph equations with high-frequency extrinsic oscillations ⋮ Asymptotic-numerical solvers for diffusion equation with time-like highly oscillatory forcing terms ⋮ Asymptotic-numerical solvers for highly oscillatory ordinary differential equations and Hamiltonian systems

Cites Work

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• A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems
• Asymptotic solvers for oscillatory systems of differential equations
• Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order
• A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators
• Asymptotic solvers for ordinary differential equations with multiple frequencies
• Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations. I
• Modulated Fourier expansions of highly oscillatory differential equations
• Adapted numerical methods for advection-reaction-diffusion problems generating periodic wavefronts
• A Gautschi-type method for oscillatory second-order differential equations
• Asymptotic solvers for second-order differential equation systems with multiple frequencies
• Adiabatic Filon-type methods for highly oscillatory second-order ordinary differential equations
• Exponentially fitted IMEX methods for advection-diffusion problems
• Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Adiabatic integrators for highly oscillatory second-order linear differential equations with time-varying eigendecomposition
• Efficient computation of delay differential equations with highly oscillatory terms
• On second-order differential equations with highly oscillatory forcing terms
• Mollified Impulse Methods for Highly Oscillatory Differential Equations
• The Method of Envelopes
• Long-Time-Step Methods for Oscillatory Differential Equations
• Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
• On highly oscillatory problems arising in electronic engineering
• Modulated Fourier expansions and heterogeneous multiscale methods
• Differential equations with general highly oscillatory forcing terms
• Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems

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