Abstract
Chapter 4 is concerned with the construction and the convergence analysis of finite difference schemes for hyperbolic initial-boundary-value problems. A key contribution of the chapter is the derivation of optimal-order bounds on the error between the analytical solution and its finite difference approximation for hyperbolic equations with variable coefficients under minimal regularity hypotheses on the coefficients and the solution, the minimal regularity hypotheses on the coefficients being expressed in terms of spaces of multipliers in anisotropic Sobolev spaces.
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Jovanović, B.S., Süli, E. (2014). Finite Difference Approximation of Hyperbolic Problems. In: Analysis of Finite Difference Schemes. Springer Series in Computational Mathematics, vol 46. Springer, London. https://doi.org/10.1007/978-1-4471-5460-0_4
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DOI: https://doi.org/10.1007/978-1-4471-5460-0_4
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