Using Optimal Time Step Selection to Boost the Order of Accuracy of Finite Difference Schemes
Bay Area Scientific Computing Day 2008, Berkeley, CA, March 29, 2008
High-order numerical methods will always be valuable for increasing the computational efficiency of numerical simulations. We present a novel technique that uses optimal time step selection to transform 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 sketch the numerical analysis argument that leads to the increase in the observed order of convergence.