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High-accuracy Stable Difference Schemes for Well-posed NBVP

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

Abstract

The single step difference schemes of the high order of accuracy for the approximate solution of the nonlocal boundary value problem (NBVP)

$$ v'\left( t \right) + Av\left( t \right) = f\left( t \right)\left( {0 \leqslant t \leqslant 1} \right),v\left( 0 \right) = v\left( \lambda \right) + \mu , 0 < \lambda \leqslant 1 $$

for the differential equation in an arbitrary Banach space E with the strongly positive operator A are presented. The construction of these difference schemes is based on the Padé difference schemes for the solutions of the initial-value problem for the abstract parabolic equation and the high order approximation formula for \( v\left( 0 \right) = v\left( \lambda \right) + \mu \). The stability, the almost coercive stability and coercive stability of these difference schemes are established.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Fatih University, 34500, Buyukcekmece Istanbul, Turkey

    Allaberen Ashyralyev

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  1. Allaberen Ashyralyev
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Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Insitute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

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Ashyralyev, A. (2009). High-accuracy Stable Difference Schemes for Well-posed NBVP. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_14

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