Approximate solution of ordinary differential equations and their systems through discrete and continuous embedded Runge-Kutta formulae and upgrading of their order
From MaRDI portal
Publication:1339288
DOI10.1016/0898-1221(94)00201-0zbMath0817.65061OpenAlexW2026607579MaRDI QIDQ1339288
Publication date: 6 August 1995
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0898-1221(94)00201-0
systemsRunge-Kutta algorithms5th order 6-stage algorithms6th order 8-stage formulas8th order 13-stage formulas
Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
Related Items
Error estimation and step size control for delay differential equation solvers based on continuously embedded Runge-Kutta-Sarafyan methods ⋮ Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Continuous approximate solution of ordinary differential equations and their systems
- An investigation of Runge-Kutta processes, and equivalence of scalar and vector cases
- New algorithms for the continuous approximate solution of ordinary differential equations and the upgrading of the order of the processes
- Improved sixth-order Runge-Kutta formulas and approximate continuous solution of ordinary differential equations
- Klassische Runge-Kutta-Nyström-Formeln mit Schrittweiten-Kontrolle für Differentialgleichungen \(\ddot x=f(t,x,\dot x)\)
- Variable-step integration methods for simulation applications
- Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
- Numerical solution of ordinary differential equations
- Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
- Interpolants for Runge-Kutta formulas
- Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
- On the Numerical Integration of Certain Differential Equations of the Second Order
- Solutions of Differential Equations by Evaluations of Functions
- Computer derivation of algebraic equations associated with runge-kutta formulas
- Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations
- Coefficients for the study of Runge-Kutta integration processes
- On the integration processes of A. Huťa