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Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Difference Schemes for Delay Parabolic Equations with Periodic Boundary Conditions

Authors : Allaberen Ashyralyev, Deniz Agirseven

Published in: Finite Difference Methods,Theory and Applications

Publisher: Springer International Publishing

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Abstract

The initial-boundary value problem for the delay parabolic partial differential equation with nonlocal conditions is studied. The convergence estimates for solutions of first and second order of accuracy difference schemes in Hölder norms are obtained. The theoretical statements are supported by a numerical example.

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previous chapter Error Estimates of the Crank-Nicolson-Polylinear FEM with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped
next chapter Some Results of FEM Schemes Analysis by Finite Difference Method
Literature
1.
Al-Mutib, A.N.: Stability properties of numerical methods for solving delay differential equations. J. Comput. and Appl. Math. 10(1), 71–79 (1984)MATHMathSciNetCrossRef
2.
Bellen, A., Jackiewicz, Z., Zennaro, M.: Stability analysis of one-step methods for neutral delay-differential equations. Numer. Math. 52(6), 605–619 (1988)MATHMathSciNetCrossRef
3.
Cooke, K.L., Györi, I.: Numerical approximation of the solutions of delay differential equations on an infinite interval using piecewise constant arguments. Comput. Math. Appl. 28, 81–92 (1994)MATHCrossRef
4.
5.
Yenicerioglu, A.F.: The behavior of solutions of second order delay differential equations. J. Math. Anal. Appl. 332(2), 1278–1290 (2007)MATHMathSciNetCrossRef
6.
Ashyralyev, A., Akca, H.: Stability estimates of difference schemes for neutral delay differential equations. Nonlinear Anal.: Theory Methods Appl. 44(4), 443–452 (2001)MATHMathSciNetCrossRef
7.
Ashyralyev, A., Akca, H., Yenicerioglu, A.F.: Stability properties of difference schemes for neutral differential equations. Differ. Equ. Appl. 3, 57–66 (2003)
8.
Liu J., Dong P., Shang G.: Sufficient conditions for inverse anticipating synchronization of unidirectional coupled chaotic systems with multiple time delays. In: Proceedings of the Chinese Control and Decision Conference, pp. 751–756. IEEE (2010)
9.
Mohamad, S., Akca, H., Covachev, V.: Discrete-time cohen-grossberg neural networks with transmission delays and impulses. Differ. Differ. Equ. Appl. Book Ser.: Tatra Mountains Math. Publ. 43, 145–161 (2009)MATHMathSciNet
10.
Ashyralyev, A., Sobolevskii, P.E.: On the stability of the delay differential and difference equations. Abstr. Appl. Anal. 6(5), 267–297 (2001)MATHMathSciNetCrossRef
11.
Ashyralyev, A., Sobolevskii, P.E.: New Difference Schemes for Partial Differential Equations. Birkhäuser Verlag, Boston (2004)MATHCrossRef
12.
Gabriella, D.B.: Delay differential equations with unbounded operators acting on delay terms. Nonlinear Anal.: Theory Methods Appl. 52(1), 1–18 (2003)MATHCrossRef
13.
Ashyralyev, A.: Fractional spaces generated by the positive differential and difference operator in a banach space. In: Tas, K., Tenreiro Machado, J.A., Baleanu, D. (eds.) Mathematical Methods in Engineering, pp. 13–22. Springer, Netherlands (2007)CrossRef
14.
Ashyralyev, A., Agirseven, D.: On convergence of difference schemes for delay parabolic equations. Comput. Math. Appl. 66(7), 1232–1244 (2013)MathSciNetCrossRef
15.
Akca, H., Shakhmurov, V.B., Arslan, G.: Differential-operator equations with bounded delay. Nonlinear Times Dig. 2, 179–190 (1995)MATHMathSciNet
16.
Akca, H., Covachev, V.: Spatial discretization of an impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms. Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Mat. 17(3), 15–16 (2009)MATHMathSciNet
17.
Ashyralyev A., Agirseven D.: Finite difference method for delay parabolic equations. In: AIP Conference Proceedings of 1389 Numerical Analysis And Applied Mathematics ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics, pp. 573–576 (2011)
18.
19.
Ashyralyev, A., Agirseven, D.: Well-posedness of delay parabolic difference equations. Adv. Differ. Equ. 2014, 1–18 (2014)MathSciNetCrossRef
20.
Ashyralyev, A., Agirseven, D.: Approximate solutions of delay parabolic equations with the Neumann condition, In: AIP Conference Proceedings, ICNAAM 2012, vol. 1479, pp. 555–558 (2012)
Metadata
Title
Difference Schemes for Delay Parabolic Equations with Periodic Boundary Conditions
Authors
Allaberen Ashyralyev
Deniz Agirseven
Copyright Year
2015
Book
Finite Difference Methods,Theory and Applications

Print ISBN: 978-3-319-20238-9

Electronic ISBN: 978-3-319-20239-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20239-6_13

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