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CMFD, 2018, Volume 64, Issue 1, Pages 1–19 (Mi cmfd343)  

A stable difference scheme for a third-order partial differential equation

A. Ashyralyevabc, Kh. Belakroumd

a Near East University, Nicosia, Turkey
b RUDN University, Moscow, Russia
c Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
d Fréres Mentouri University, Constantine, Algeria

Abstract: The nonlocal boundary-value problem for a third order partial differential equation
\begin{equation*} \{ \begin{array}{l} \frac{d^3u(t)}{dt^3}+A\frac{du(t)}{dt}=f(t),\quad 0<t<1,
u(0)=\gamma u(\lambda)+\varphi,\qquad u'(0)=\alpha u'(\lambda)+\psi,\quad|\gamma|<1,
u"(0)=\beta u"(\lambda)+\xi,\qquad|1+\beta\alpha|>|\alpha+\beta|,\quad0<\lambda\leq1, \end{array} . \end{equation*}
in a Hilbert space $H$ with a self-adjoint positive definite operator $A$ is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for one- and two-dimensional third order partial differential equations are provided.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
Ministry of Education and Science of the Republic of Kazakhstan BR05236656


DOI: https://doi.org/10.22363/2413-3639-2018-64-1-1-19

Full text: PDF file (415 kB)
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UDC: 517.9

Citation: A. Ashyralyev, Kh. Belakroum, “A stable difference scheme for a third-order partial differential equation”, Differential and functional differential equations, CMFD, 64, no. 1, Peoples' Friendship University of Russia, M., 2018, 1–19

Citation in format AMSBIB
\Bibitem{AshBel18}
\by A.~Ashyralyev, Kh.~Belakroum
\paper A stable difference scheme for a~third-order partial differential equation
\inbook Differential and functional differential equations
\serial CMFD
\yr 2018
\vol 64
\issue 1
\pages 1--19
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd343}
\crossref{https://doi.org/10.22363/2413-3639-2018-64-1-1-19}


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