High-Order Numerical Methods from Low-Order Stencils for Time-Dependent PDEs
Institute of High Performance Computing, A*STAR, Singapore, October 10, 2007
High-order numerical methods are invaluable for increasing the computational efficiency of numerical simulations. It is no surprise that a great deal of effort in numerical PDEs continues to be focused on developing high-order numerical schemes. In this talk, we discuss a novel technique based on optimal time step selection for boosting low-order finite-difference schemes into higher-order numerical methods for a class of linear, time-dependent PDEs. We demonstrate the utility of this technique on several classical hyperbolic and parabolic problems in one and more space dimensions and explain the observed orders of convergence through straightforward numerical analysis arguments.