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A fourth-order alternating-direction method for difference schemes with nonlocal condition*

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Abstract

We consider a finite-difference scheme of fourth-order accuracy for the two-dimensional Poisson equation in a rectangular domain with nonlocal integral conditions in one coordinate direction. The system of finite-difference equations is solved using a generalization of the Peaceman–Rachford alternating-direction implicit method. We prove the convergence of the method and estimate the rate of convergence by using the structure of the spectrum of one-dimensional difference operators with nonlocal integral conditions.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania

    M. Sapagovas & O. Štikonienė

Authors
  1. M. Sapagovas
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  2. O. Štikonienė
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Correspondence to M. Sapagovas.

Additional information

*The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-73/09.

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Sapagovas, M., Štikonienė, O. A fourth-order alternating-direction method for difference schemes with nonlocal condition*. Lith Math J 49, 309–317 (2009). https://doi.org/10.1007/s10986-009-9057-5

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  • DOI: https://doi.org/10.1007/s10986-009-9057-5

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