Extensions of Optimal Time Step Selection: Boosting the Accuracy of Finite-Difference Methods for Variable Coefficient PDEs and Systems of PDEs
Institute of High Performance Computing, A*STAR, Singapore, September 11, 2008
In its original incarnation, the optimal time step (OTS) selection technique makes it possible to transform formally low-order finite-difference schemes into high-order numerical methods for time-dependent scalar PDEs, in any number of space dimensions, on both regular and irregular domains. For example, OTS selection achieves high-order accuracy using simple schemes based on forward Euler time integration and low-order stencils for spatial derivatives. In this talk, we present recent extensions of OTS selection to variable coefficient PDEs and systems of PDEs. We also demonstrate its utility for non-forward Euler time integration schemes. The observed orders of accuracy will be explained using straightforward numerical analysis arguments.