Digital Filter Stepsize Control in DASPK and its Effect on Control Optimization Performance∗

Overview It has long been known that the solutions produced by adaptive solvers for ordinary differential (ODE) and differential algebraic (DAE) systems, while generally reliable, are not smooth with respect to perturbations in initial conditions or other problem parameters. Söderlind and Wang [12, 13] have recently developed a digital filter stepsize controller that has a theoretical basis from control and appears to result in a much smoother dependence of the solution on problem parameters. This property seems particularly important in the control and optimization of dynamical systems, where the optimizer is generally expecting the DAE solver to return solutions that vary smoothly with respect to the parameters. We have implemented the digital filter stepsize controller in the DAE solver DASPK3.1, and used the new solver for the optimization of dynamical systems. The improved performance of the optimizer, as a result of the new stepsize controller, is demonstrated on a biological problem regarding the heat shock response of Escherichia coli.