Step Change Strategies for Multistep Methods
Ole Østerby
- 01 Aug 1985
Vol. 14, Iss: 196
TL;DR: It is shown that the commonly used formulas for calculating the new step sizes are not correct for multistep methods and correct formulas are derived for Adams methods.
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Abstract: When a system of ordinary differential equations is solved using a step-by-step method it is often desirable to change the step size during the course of the integration. We show that the commonly used formulas for calculating the new step sizes are not correct for multistep methods and we derive correct formulas for Adams methods.
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Citations
•Dissertation
Use of sinusoidal predictors for time domain simulation of AC power systems
Pierre-Marie Gibert
- 30 Nov 2018
TL;DR: The sinusoidal predictors method, integrated into the reference solver SUNDIALS IDA and interfaced with an industrial simulation engine, enables to very significantly accelerate simulations in comparison with a classical implementation.
2
Construction and benchmarking of adaptive parameterized linear multistep methods
Josefine Olander,Erik Jonsson Glans +1 more
- 01 Jan 2016
TL;DR: General numerical solvers based on a new way to define all k-step linear multistep methods of order k and k+1 in a parametric form that builds in variable step-size have been implemented.
References
•Book
Numerical Initial Value Problems in Ordinary Differential Equations
C. William Gear
- 01 Sep 1971
4.1K
Computational techniques for ordinary differential equations
I. Gladwell,D. K. Sayers +1 more
- 01 Jan 1980
122
Characterization of Optimal Stepsize Sequences for Methods for Stiff Differential Equations
TL;DR: From the characterization of the optimal stepsize sequences for stiff systems one can conclude that the stepsize sequence obtained with a fixed bound on the local error per unit step is far from optimal.
27
Global Error Estimates for Ordinary Differential Equations
Lawrence F. Shampine,H. A. Watts +1 more
TL;DR: This paper describes a way of estimating the global error reliably while still solving the problem with acceptable efficiency in a Fortran program called GERK.