Intermediate boundary conditions for time-split methods applied to hyperbolic partial differential equations

When time-split or fractional step methods are used to solve partial differential equations numerically, nonphysical intermediate solutions are introduced for which boundary data must often be specified. Here the appropriate boundary conditions are derived for splittings of hyperbolic problems into subproblems with disparate wave speeds. Numerical experiments are performed for the one-dimensional shallow water equations, a quasilinear system with inflow-outflow boundaries. Stability of the initial-boundary value problem is demonstrated for boundary conditions of the type derived here.