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Finite Difference Approximation of Parabolic Problems

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Book cover Analysis of Finite Difference Schemes

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 46))

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Abstract

Chapter 3 is concerned with the construction and the convergence analysis of finite difference schemes for parabolic initial-boundary-value problems. The central contribution of the chapter is the derivation of optimal-order bounds on the error between the analytical solution and its finite difference approximation for parabolic 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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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Boško S. Jovanović

  2. Mathematical Institute, University of Oxford, Oxford, UK

    Endre Süli

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  1. Boško S. Jovanović
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Jovanović, B.S., Süli, E. (2014). Finite Difference Approximation of Parabolic 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_3

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