A new numerical method for the integration of highly oscillatory second-order ordinary differential equations

DOI10.1016/0168-9274(93)90131-AzbMath0808.65081OpenAlexW2037354281MaRDI QIDQ1308560

V. Pereyra

Publication date: 6 January 1994

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

Full work available at URL: https://doi.org/10.1016/0168-9274(93)90131-a

zbMATH Keywords

numerical resultsconsistencyoscillatory solutionsmultistep method\(P\)-stabilityprinciple of coherencecovergencehighly oscillatory second-order ordinary differential equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (11)

Multistep variable methods for exact integration of perturbed stiff linear systems ⋮ Numeric multistep variable methods for perturbed linear system integration ⋮ Parallel one-step methods with minimal parallel stages ⋮ An algorithm for exact integration of some forced and damped oscillatory problems, based in the \(\tau \)-functions ⋮ VSVO multistep formulae adapted to perturbed second-order differential equations ⋮ Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations. ⋮ A new approach to the construction of multirevolution methods and their implementation ⋮ Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method ⋮ A variable-step Numerov method for the numerical solution of the Schrödinger equation ⋮ Multistep numerical methods for the integration of oscillatory problems in several frequencies ⋮ A new method for exact integration of some perturbed stiff linear systems of oscillatory type

Uses Software

• Maple
• ODEPACK

Cites Work

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• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• A study of extrapolation methods based on multistep schemes without parasitic solutions
• Stabilization of Cowell's method
• Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• A modified numerov integration method for second order periodic initial-value problems

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