Runge-Kutta pairs for periodic initial value problems

DOI10.1007/BF02243849zbMath0787.65052OpenAlexW64179385MaRDI QIDQ1310616

Ch. Tsitouras, S. N. Papakostas, George Papageorgiou

Publication date: 24 May 1994

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02243849

zbMATH Keywords

performanceperiodic solutionsinitial value problemstability intervalexplicit \(s\)-stage Runge-Kutta formulaephase- lag

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (16)

On ninth order, explicit Numerov-type methods with constant coefficients ⋮ Explicit Runge-Kutta pairs appropriate for engineering applications ⋮ On fitted modifications of Runge-Kutta-Nyström pairs ⋮ Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors ⋮ A high-order explicit Runge-Kutta pair for initial value problems with oscillating solutions ⋮ A family of fifth-order Runge-Kutta pairs ⋮ Explicit, eighth-order, four-step methods for solving \(y^{\prime\prime}=f(x, y)\) ⋮ Explicit Runge-Kutta methods for starting integration of Lane-Emden problem ⋮ Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits ⋮ Evolutionary derivation of Runge-Kutta pairs for addressing inhomogeneous linear problems ⋮ Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives ⋮ A parameter study of explicit Runge-Kutta pairs of orders 6(5) ⋮ Bounds for variable degree rational \(L_\infty\) approximations to the matrix exponential ⋮ Runge-Kutta pairs for periodic initial value problems ⋮ Optimized Runge-Kutta pairs for problems with oscillating solutions ⋮ Phase-fitted Runge-Kutta pairs of orders 8(7)

Cites Work

• Unnamed Item
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• A family of embedded Runge-Kutta formulae
• Stabilization of Cowell's classical finite difference method for numerical integration
• Runge-Kutta pairs for periodic initial value problems
• An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
• Global error estimation with Runge-Kutta triples
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Some Runge–Kutta Formula Pairs
• Damping and phase analysis for some methods for solving second-order ordinary differential equations
• Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• A one-step method for direct integration of structural dynamic equations
• On Runge-Kutta processes of high order

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