
A stable difference scheme for a thirdorder partial differential equation
A. Ashyralyev^{abc}, Kh. Belakroum^{d} ^{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 boundaryvalue 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,\qquad1+\beta\alpha>\alpha+\beta,\quad0<\lambda\leq1,
\end{array}
.
\end{equation*}
in a Hilbert space $H$ with a selfadjoint positive definite operator $A$ is considered. A stable threestep 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 twodimensional third order partial differential equations are provided.
DOI:
https://doi.org/10.22363/241336392018641119
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Citation:
A. Ashyralyev, Kh. Belakroum, “A stable difference scheme for a thirdorder 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~thirdorder partial differential equation
\inbook Differential and functional differential equations
\serial CMFD
\yr 2018
\vol 64
\issue 1
\pages 119
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd343}
\crossref{https://doi.org/10.22363/241336392018641119}
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