High-Order Accurate Finite Difference Schemes Via Optimal Time Step Selection
SIAM Annual Meeting, San Diego, CA, July 10, 2008
This talk presents a novel technique based on optimal time step selection that transforms low-order finite-difference schemes into high-order numerical methods for time-dependent PDEs. For example, optimal time step selection can achieve high-order accuracy using simple schemes based on forward Euler time integration and low-order stencils for spatial derivatives. We demonstrate the utility of optimal time step selection on several classical PDEs in one and two space dimensions (on both regular and irregular domains) and explain the observed orders of convergence through straightforward numerical analysis arguments.