Stable, high-order discretization for evolution of the wave equation in 1+1 dimensions
We carry forward the approach of Alpert, Greengard, and Hagstrom to construct stable high-order explicit discretizations for the wave equation in one space and one time dimension. They presented their scheme as an integral form of the Lax-Wendroff method. Our perspective is somewhat different from theirs; our focus is on the discretization of the evolution formula rather than on its form (integral, differential, etc.). A key feature of our approach is the independent computation of three discretizations, one for bulk (away from boundaries) propagation, one for propagation near boundaries, and a projection operator to enforce boundary conditions. This is done in a way that is straightforward to extend to more space dimensions. (C) 2003 Elsevier Inc. All rights reserved.
small-cell problem stability