(542g) Squeeze Functional Approach for Adaptive Step Size in Solving Stiff ODE/Dae Problems
AIChE Annual Meeting
Wednesday, November 16, 2022 - 5:24pm to 5:43pm
In this paper we introduce an adaptive step size approach based on a dynamic error estimate obtained from a pair of âsqueezeâ functionals that bound the true solution and its Taylor approximation (of desired order). By monitoring the size and growth rate of the bound gap, relative to specified tolerances, it can be determined whether the Taylor approximations remain sufficiently accurate, and then the length of the time step can be adapted accordingly. Results of preliminary tests of this approach on a variety of stiff ODE problems will be presented, indicating that it is more efficient and reliable than standard Matlab solvers (e.g., ode15s, ode23s, ode23t) for stiff problems. Test problems include a flame propagation problem , the Robertsonâs chemical reaction model , the van der Pol oscillator, a double pendulum problem and a three-body problem.
 Shampine, L. F. and M. W. Reichelt, âThe MATLAB ODE Suite,â SIAM Journal on Scientific Computing, 18, 1-22 (1998).
 Jannelli A., Fazio R. âAdaptive stiff solvers at low accuracy and complexityâ, J. of Computational and Applied Mathematics, 191, 246-258 (2006).
 Robertson, H.H. The solution of a set of reaction rate equations. In Numerical Analysis: An Introduction, J. Walsh, Ed., Academic Press: London, UK, 1966.