Event Location for Ordinary Di erential Equations
نویسنده
چکیده
An initial value problem for y0 = f(t; y) may have an associated event function g(t; y). An event is said to occur at t when g(t ; y(t )) = 0. We consider problems for which the de nition of f(t; y) changes at the time of an event. A number of solvers locate events and restart the integration there so as to deal with the changes in f , but there is little theoretical support for what is done. Here we prove that with reasonable assumptions about the problem and the solver, the error of the numerical solution is qualitatively the same whether or not events occur. Numerical results obtained with a wide range of solvers con rm the theory developed here.
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