A note on a diagonally implicit Runge-Kutta-Nyström method

DOI10.1016/0377-0427(87)90208-1zbMath0637.65065OpenAlexW2030224870MaRDI QIDQ1098578

B. P. Sommeijer

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90208-1

zbMATH Keywords

direct methodP-stabilitysecond-order initial value problemfourth-order accurate diagonally implicit Runge-Kutta-Nyström methodslargest interval of periodicity

Mathematics Subject Classification ID

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)

Related Items (9)

Embedded diagonally implicit Runge-Kutta-Nystrom 4(3) pair for solving special second-order IVPs ⋮ Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems ⋮ A two-stage fourth-order ``almost P-stable method for oscillatory problems ⋮ A phase- and amplification-fitted 5(4) diagonally implicit Runge-Kutta-Nyström pair for oscillatory systems ⋮ A zero-dissipative phase-fitted fourth order diagonally implicit Runge-Kutta-Nyström method for solving oscillatory problems ⋮ Quintic \(C^2\)-spline integration methods for solving second-order ordinary initial value problems ⋮ Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials ⋮ Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations ⋮ Unnamed Item

Cites Work

• A theory for Nyström methods
• Méthodes de Nystrom pour l'équation différentielle y=f(x,y)
• Unconditionally stable methods for second order differential equations
• Stabilization of Cowell's method
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• Implicit Runge-Kutta Processes

This page was built for publication: A note on a diagonally implicit Runge-Kutta-Nyström method