Multidimensional Stepsize Control

Abstract

AbstractOptimization problems in technical simulation often lead to boundary value problems for systems of highly nonlinear ordinary differential equations with piecewise defined right hand sides and a large number of exceptional points with reduced differentiability. Classical integration schemes show a poor performance due to the large number of restarts of the integrator; integration intervals end before the stepsize control has stabilized. The new approach does not only use the information of the preceeding integration step for stepsize control, but also information from the preceeding iteration step, if the boundray value problem is solved by an iterative algorithm. Multistage search techniques improve the efficiency of the determination of the exceptional points. These new techniques are tightly coupled with the progress of the Newton process. The numerical solution of the boundary value problem is by the new multiple shooting code JANUS which fully exploits the new integration techniques.