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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 – de Gruyter
Published: Apr 1, 2005
Keywords: Finite difference schemes,; integral identities,; interface problems
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