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A collocation-Galerkin method for a first order hyperbolic equation with space and time dependent coefficient

Authors: David Archer and Julio César Díaz
Journal: Math. Comp. 38 (1982), 37-53
MSC: Primary 65M60; Secondary 65N35
MathSciNet review: 637285
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Abstract: A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree $ r - 1$ on [0, 1] with respect to the weight function $ x(1 - x)$. Optimal $ {L^\infty }({L^2})$-norm estimates of the error are derived.

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Article copyright: © Copyright 1982 American Mathematical Society