Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I

Abstract

Easily checkable sufficient stability criteria are obtained for explicit dissipative approximations to mixed initial-boundary value problems associated with the system u t = A u x {u_t} = A{u_x} in the quarter plane x ⩾ 0 x \geqslant 0 , t ⩾ 0 t \geqslant 0 . The criteria are given entirely in terms of the boundary conditions for the outflow unknowns. The results imply that certain well-known boundary conditions, when used in combination with any (stable) dissipative scheme, always maintain stability.