Explicit Runge-Kutta methods for initial value problems with oscillating solutions

DOI10.1016/S0377-0427(96)00103-3zbMath0871.65073OpenAlexW1997523150MaRDI QIDQ5961655

Juan I. Montijano, Manuel Calvo, Luis Rández, J. M. Franco

Publication date: 7 October 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(96)00103-3

zbMATH Keywords

stabilitynumerical experimentsoscillating solutionsfirst-order systemsdispersion and dissipation errorsembedded Runge-Kutta methodsperiodic initial value problemsstepsize estimator

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) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (18)

SDIRK methods for stiff ODEs with oscillating solutions ⋮ Exponential fitting for interpolation of oscillatory functions. A numerical approach ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ An explicit exponential integrator based on Faber polynomials and its application to seismic wave modeling ⋮ Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations. ⋮ Minimum storage Runge-Kutta schemes for computational acoustics. ⋮ A high-order explicit Runge-Kutta pair for initial value problems with oscillating solutions ⋮ Sixth order non-dissipativeC¹spline collocation method for oscillatory ordinary initial value problems ⋮ Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations ⋮ A new minimum storage Runge-Kutta scheme for computational acoustics ⋮ Runge-Kutta projection methods with low dispersion and dissipation errors ⋮ A symplectic Runge-Kutta-Nyström method with minimal phase-lag ⋮ FOURTH ORDER SYMPLECTIC INTEGRATION WITH REDUCED PHASE ERROR ⋮ Numerical computation of the coefficients in exponential fitting ⋮ High-accuracy non-dissipative extended one-step methods for oscillatory problems ⋮ Adapted explicit two-step peer methods ⋮ Non-dissipative extended one-step methods for oscillatory problems ⋮ Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• On the numerical integration of second-order initial value problems with a periodic forcing function
• High order embedded Runge-Kutta formulae
• A low-order embedded Runge-Kutta method for periodic initial-value problems
• A polyvalent Runge-Kutta triple
• Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
• Phase-Lag Analysis of Implicit Runge–Kutta Methods
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• A one-step method for direct integration of structural dynamic equations

This page was built for publication: Explicit Runge-Kutta methods for initial value problems with oscillating solutions