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Sib. Zh. Vychisl. Mat., 2010, Volume 13, Number 4, Pages 387–401 (Mi sjvm414)  

Asymptotic error estimates of a linearized projection-difference method for a differential equation with a monotone operator

P. V. Vinogradovaa, A. G. Zarubinb

a Far Eastern State Transport University, Khabarovsk
b Pacific National University

Abstract: In this paper, we study a projection-difference method for the Cauchy problem for an operator-differential equation with a self-adjoint leading operator $A(t)$ and a non-linear monotone subordinate operator $K(\cdot)$ in a Hilbert space. This method leads to solving a system of linear algebraic equations at each time level. Error estimates for the approximate solutions as well as for the fractional powers of the operator $A(t)$ are obtained. The method is applied to a model parabolic problem.

Key words: operator-differential equation, monotone operator, difference scheme, convergence rate, Faedo–Galerkin method.

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English version:
Numerical Analysis and Applications, 2010, 3:4, 317–328

UDC: 519.63
Received: 19.01.2010

Citation: P. V. Vinogradova, A. G. Zarubin, “Asymptotic error estimates of a linearized projection-difference method for a differential equation with a monotone operator”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 387–401; Num. Anal. Appl., 3:4 (2010), 317–328

Citation in format AMSBIB
\Bibitem{VinZar10}
\by P.~V.~Vinogradova, A.~G.~Zarubin
\paper Asymptotic error estimates of a~linearized projection-difference method for a~differential equation with a~monotone operator
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 4
\pages 387--401
\mathnet{http://mi.mathnet.ru/sjvm414}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 4
\pages 317--328
\crossref{https://doi.org/10.1134/S1995423910040038}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650374802}


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