Multistep-Galerkin methods for hyperbolic equations

Dougalis, Vassilios A.

doi:10.1090/S0025-5718-1979-0521277-5

Multistep-Galerkin methods for hyperbolic equations
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by Vassilios A. Dougalis PDF

Math. Comp. 33 (1979), 563-584 Request permission

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. ${L^2}$-error bounds of optimal order in space and time are achieved for large classes of such multistep methods.

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