Multistep-Galerkin Methods for Hyperbolic Equations

Abstract
Multistep methods for first- and second-order ordinary differential equations are used for the full discretizations of standard Galerkin approximations to the initial-periodic boundary value problem for first-order linear hyperbolic equations in one space dimension and to the initial-boundary value problem for second-order linear selfadjoint hyperbolic equations in many space dimensions. -error bounds of optimal order in space and time are achieved for large classes of such multistep methods.