Using Optimal Time Step Selection to Boost the Accuracy of Finite-Difference Schemes for Variable-Coefficient and Systems of Time-Dependent PDEs
SIAM Annual Meeting, Denver, CO, July 10, 2009
An optimal choice of time step can be used to boost the order of accuracy of formally low-order finite-difference schemes for time-dependent scalar PDEs. This talk presents extensions of the technique of optimal time step selection to variable-coefficient and systems of PDEs. For variable-coefficient PDEs, higher-order accuracy is achieved by combining optimal time step selection with optimal grid choice. For systems of PDEs, a simple synchronization procedure can be used to achieve higher-order accuracy when the individual PDEs have different optimal time steps. We demonstrate the utility of these extensions by applying them to several example PDEs and explain the observed orders of convergence explained via straightforward numerical analysis arguments.