RDEAM: An Adams ODE Code with Root Solving Capability

摘要

Our goal has been to develop a robust root solving ODE code; that is, one which solves differential equations and isolates roots of specified event functions in the solution variables. This work concentrated on computational and software issues aimed at enhancing the reliability of locating the roots in question. Thus the primary emphasis has been placed on providing a capability which has not previously been available, and one which is needed for handling difficult and sensitive root problems. There is no doubt that we are doing a lot of work in attempting to guarantee the finding of all roots, regardless of the problem formulation. This effort is what we have referred to as the refined or sophisticated root searching procedure. It is relatively expensive, but necessary, for some problems. A less expensive and more conventional mode of operation for the root solving is also available to the user. This approach skips the refined root searching so that root detection is based solely on looking for a sign change at the endpoints of the integration step size interval. This will work well provided there is a good correlation between the step sizes taken for the integration problem and the scale or variation of the event functions. Otherwise roots are likely to be missed. 20 refs. (ERA citation 11:012523)