The art of writing a Runge-Kutta code. II

DOI10.1016/0096-3003(79)90001-8zbMath0431.68039OpenAlexW1970303458WikidataQ127957369 ScholiaQ127957369MaRDI QIDQ1138376

H. A. Watts, Lawrence F. Shampine

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0096-3003(79)90001-8

zbMATH Keywords

softwareRunge-Kutta methodsRKF 45

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Theory of software (68N99)

Related Items (21)

A fourth order Runge–Kutta RK(4,4) method with error control ⋮ GIP integrators for matrix Riccati differential equations ⋮ Control of step size and order in extrapolation codes ⋮ On a quadratic equation of state and a universe mildly bouncing above the Planck temperature ⋮ Solving complex-valued differential systems ⋮ Better software for ODEs ⋮ Error estimation and control for ODEs ⋮ A new Runge Kutta RK(4, 4) method ⋮ Torsion, an alternative to dark matter? ⋮ Numerical strategies for the system of first-order IVPS using the RK–Butcher algorithm ⋮ TORSION, AN ALTERNATIVE TO THE COSMOLOGICAL CONSTANT? ⋮ A friendly Fortran DDE solver ⋮ Software based on explicit RK formulas ⋮ RKF45 ⋮ Recent advances in methods for numerical solution of O.D.E. initial value problems ⋮ Optimal control of singular systems using the rk–butcher algorithm ⋮ Initial value problems for ODEs in problem solving environments ⋮ Step size control in the numerical solution of stochastic differential equations ⋮ Starting step size for an ODE solver ⋮ Unnamed Item ⋮ The step sizes used by one-step codes for ODEs

Uses Software

• IMSL Numerical Libraries

Cites Work

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• Quadrature and Runge-Kutta formulas
• Local error control in codes for ordinary differential equations
• Detecting stiffness with the Fehlberg (4,5) formulas
• Numerical solution of ordinary simultaneous differential equations of the 1st order using a method for automatic step change
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• A User’s View of Solving Stiff Ordinary Differential Equations
• On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations
• Comparing numerical methods for stiff systems of O.D.E:s
• Global Error Estimates for Ordinary Differential Equations
• Solving Nonstiff Ordinary Differential Equations—The State of the Art
• Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods
• Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations
• Limiting Precision in Differential Equation Solvers
• The automatic integration of ordinary differential equations
• Comparing Numerical Methods for Ordinary Differential Equations
• Comparing Error Estimators for Runge-Kutta Methods

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