Hopscotch Difference Methods for Nonlinear Hyperbolic Systems
by A. R. Gourlay, J. L. Morris
In a recent series of papers, one of the authors has developed and demonstrated properties of a computational algorithm for solving partial differential equations. This process, known as the hopscotch algorithm, has been studied particularly with reference to the efficient integration of parabolic and elliptic problems. In the present paper attention is directed to the application of the technique to the numerical integration of first-order nonlinear hyperbolic systems. While maintaining the properties of the hopscotch process as applied to parabolic problems, it is shown that one of the novel schemes generated by this approach has an added bonus, namely, maximum stability for a variable choice of damping or pseudoviscous term. This property should be of particular value in the solution of problems with shocks. A class of hopscotch Lax-Wendroff schemes is also studied.