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I. T. Angelova, L. G. Vulkov

High-order difference schemes based on new Marchuk integral identities for one-dimensional interface problems

Keywords: Finite difference schemes, integral identities, interface problems

High-order finite difference approximations of the solution and the flux to model interface problems in one-dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O(h ²), O(h ⁴),… accuracy are derived. Numerical integration procedures using Lobatto quadratures for computing three-point schemes of any prescribed order of accuracy are developed. A rigorous rate of convergence analysis is presented. Numerical experiments confirm the theoretical results.

Journal of Numerical Mathematics, Walter de Gruyter

Print ISSN: 1570-2820
Volume: 13, 04/2005
Pages: 1 - 18

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