EVOLUTION OF SCALAR FIELDS FROM CHARACTERISTIC DATA

We present a new algorithm for solving nonlinear wave equations when initial data is specified on characteristic surfaces. The algorithm is directly applicable to hyperbolic systems such as Maxwell, Yang-Mills, and gravitational fields. The basic principles should also be applicable to hydrodynamics. It is an especially effective approach for studying radiation fields. We show that this method is stable, globally convergent to second order in the grid spacing, and satisfies an energy conservation law. We carry out numerical studies of scalar wave equations with nonlinear self-interactions for some examples of physical interest. We observe nonlinear phenomena such as backscattering, radiative tail decay, and approximate analogues to solitons in three dimensions. © 1992.