Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
An extrapolation step-size monitor for solving ordinary differential equations
ACM '74 Proceedings of the 1974 annual conference - Volume 1
Note on the startup of ODE solvers
ACM SIGNUM Newsletter
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In the design of a step-size and order monitor for the numerical solution of ordinary differential equations, the conventional wisdom holds that the monitor should start with a cautious first-order method. For example, Gear [1], Hindmarsh [2], Schryer [3], and Shampine and Gordon [4] require that the initial successful integration be accomplished with a first-order method. Of course these authors have other good reasons for their design besides mere caution. However, for stiff ODE's we will show that this restriction can lead the monitor to abandon perfectly reasonable problems.