On the numerical integration of second-order initial value problems with a periodic forcing function

DOI10.1007/BF02252512zbMath0589.65064OpenAlexW1527630372MaRDI QIDQ1074317

B. P. Sommeijer, P. J. van der Houwen, Karl Strehmel, Rüdiger Weiner

Publication date: 1986

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02252512

zbMATH Keywords

periodic solutionsforced oscillationpredictor-correctorNumerical examplesRunge-Kutta-Nyströmreduced phase lag methodssecond- order

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

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Cites Work

• Unnamed Item
• Phase properties of high order, almost P-stable formulae
• Nichtlineare Stabilität und Phasenuntersuchung adaptiver Nyström- Runge-Kutta-Methoden (Nonlinear stability and phase analysis for adaptive Nyström-Runge-Kutta methods)
• Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y=f(t,y)\)
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• Phase-lag analysis for a family of two-step methods for second order periodic initial value problems
• Stabilization of Cowell's classical finite difference method for numerical integration
• A theory for Nyström methods
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Predictor-corrector Methods with Improved Absolute Stability Regions
• Damping and phase analysis for some methods for solving second-order ordinary differential equations
• Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems
• A one-step method for direct integration of structural dynamic equations