Equilibrium states of Runge Kutta schemes-Reference-Cited by-同舟云学术

Equilibrium states of Runge Kutta schemes

Published:1985-09 Issue:3 Volume:11 Page:289-301
ISSN:0098-3500
Container-title:ACM Transactions on Mathematical Software
language:en
Short-container-title:ACM Trans. Math. Softw.

Author:

Hall George¹

Affiliation:

1. Department of Mathematics, The University, Manchester M13 9PL, England

Abstract

Understanding the behavior of Runge-Kutta codes when stability considerations restrict the stepsize provides useful information for stiffness detection and other implementation details. Analysis of equilibrium states on test problems is presented which provides predictions and insights into this behavior. The implications for global error are also discussed.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Link

https://dl.acm.org/doi/pdf/10.1145/214408.214424

Reference6 articles.

1. HALL G. AND SULEIMAN M.B. A single code for the solution of stiff and non-stiff ODE's. SIAM J. Sci. Stat. Comput. (to be published). HALL G. AND SULEIMAN M.B. A single code for the solution of stiff and non-stiff ODE's. SIAM J. Sci. Stat. Comput. (to be published).

2. Characterization of Optimal Stepsize Sequences for Methods for Stiff Differential Equations

3. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations

4. Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods

Cited by 45 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A step-size selection strategy for explicit Runge–Kutta methods based on Lyapunov exponent theory;Journal of Computational and Applied Mathematics;2016-01

2. References;General Linear Methods for Ordinary Differential Equations;2009-08-10

3. Approximation of Attractors by a Variable Time-Stepping Algorithm for Runge-Kutta Methods;Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007);2007-09

4. Mean-square stability properties of an adaptive time-stepping SDE solver;Journal of Computational and Applied Mathematics;2006-10

5. Time-step selection algorithms: Adaptivity, control, and signal processing;Applied Numerical Mathematics;2006-03