Finite difference schemes for conservation laws

Abstract : We study finite difference approximations to weak solutions of the Cauchy problem for hyperbolic systems of conservation laws in one space dimension. We establish stability in the total variation norm and convergence for a class of hybridized schemes which employ the random choice scheme together with perturbations of classical conservative schemes. We also establish partial stability results for classical conservative schemes. Our approach is based on an analysis of finite difference operators on local and global wave configurations. (Author)

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