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Year 2020, , 90 - 95, 30.12.2020
https://doi.org/10.47086/pims.778004

Abstract

References

  • [1] A. Ashyralyev, and H. O. Fattorini, On uniform difference schemes for the second-order singular perturbation problem in Banach spaces, SIAM. J. Math. Anal., 23 (1992) 29-54.
  • [2] A. Ashyralyev, and N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations, Numer. Func. Anal. Op., 25 (2004) 439-462.
  • [3] A. Ashyralyev, and N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations, Numer. Func. Anal. Op., 25 (2004) 439-462.
  • [4] A. Ashyralyev, Nonlocal boundary-value problems or abstract parabolic equations: wellposedness in Bochner spaces, J. Evol. Equ., 6 (2006), 1-28.
  • [5] A. Ashyralyev, and Y. Ozdemir, On nonlocal boundary value problems hyperbolic-parabolic equations Taiwan. J. Math., 4 (2007), 1075-1089.
  • [6] A. Ashyralyev, and O. Gercek, Nonlocal boundary value problems of elliptic-parabolic differential and difference equations, Discrete. Dyn. Nat. Soc., 2008 (2008), 1-16.
  • [7] A. Ashyralyev, and A. Sirma, Nonlocal boundary value problems for Shrödinger equations, Comput. Math. Appl., 55 (2008), 392-407.
  • [8] A. Ashyralyev, and B. Hicdurmaz, A note on the fractional Schrödinger differential equatios, Kybernetes, 40 (2011), 736-750.
  • [9] A. Ashyralyev and O. Yıldırım, On multipoint nonlocal boundary value problems for hyperbolic differential and difference equations, Taiwan. J. Math., 14 (2010), 165-194.
  • [10] Y. Ozdemir, and M. Kucukunal, A note on nonlocal boundary value problems for hyperbolic Schrödinger equations, Abstr. Appl. Anal., 2012 (2012), 1-12.
  • [11] A. Ashyralyev, and O. Yıldırım, A note on the second order accuracy stable difference schemes for the nonlocal boundary value hyperbolic problem, Abstr. Appl. Anal., 2012 (2012), 1-29.
  • [12] A. A. Samarskii, and E. S. Nikolaev, Numerical Methods for Grid Equations, Vol. 2 Iterative Methods, Birk¨auser, Basel, 1989.

On The Stability of Nonlocal Boundary Value Problem for Schrödinger-Parabolic Equations

Year 2020, , 90 - 95, 30.12.2020
https://doi.org/10.47086/pims.778004

Abstract

In the present article, a problem for a Schrödinger-parabolic equation with nonlocal boundary value condition is considered. The stability estimates are established for the solution of Schrödinger-parabolic problem. In applications, the stability estimates of mixed type nonlocal boundary value problem for Schrödinger-parabolic equations are constructed. On the other hand, an example is considered and some error results of numerical experiments are presented in order to verify theoretical statements.

References

  • [1] A. Ashyralyev, and H. O. Fattorini, On uniform difference schemes for the second-order singular perturbation problem in Banach spaces, SIAM. J. Math. Anal., 23 (1992) 29-54.
  • [2] A. Ashyralyev, and N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations, Numer. Func. Anal. Op., 25 (2004) 439-462.
  • [3] A. Ashyralyev, and N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations, Numer. Func. Anal. Op., 25 (2004) 439-462.
  • [4] A. Ashyralyev, Nonlocal boundary-value problems or abstract parabolic equations: wellposedness in Bochner spaces, J. Evol. Equ., 6 (2006), 1-28.
  • [5] A. Ashyralyev, and Y. Ozdemir, On nonlocal boundary value problems hyperbolic-parabolic equations Taiwan. J. Math., 4 (2007), 1075-1089.
  • [6] A. Ashyralyev, and O. Gercek, Nonlocal boundary value problems of elliptic-parabolic differential and difference equations, Discrete. Dyn. Nat. Soc., 2008 (2008), 1-16.
  • [7] A. Ashyralyev, and A. Sirma, Nonlocal boundary value problems for Shrödinger equations, Comput. Math. Appl., 55 (2008), 392-407.
  • [8] A. Ashyralyev, and B. Hicdurmaz, A note on the fractional Schrödinger differential equatios, Kybernetes, 40 (2011), 736-750.
  • [9] A. Ashyralyev and O. Yıldırım, On multipoint nonlocal boundary value problems for hyperbolic differential and difference equations, Taiwan. J. Math., 14 (2010), 165-194.
  • [10] Y. Ozdemir, and M. Kucukunal, A note on nonlocal boundary value problems for hyperbolic Schrödinger equations, Abstr. Appl. Anal., 2012 (2012), 1-12.
  • [11] A. Ashyralyev, and O. Yıldırım, A note on the second order accuracy stable difference schemes for the nonlocal boundary value hyperbolic problem, Abstr. Appl. Anal., 2012 (2012), 1-29.
  • [12] A. A. Samarskii, and E. S. Nikolaev, Numerical Methods for Grid Equations, Vol. 2 Iterative Methods, Birk¨auser, Basel, 1989.
There are 12 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

Yildirim Ozdemir 0000-0003-2767-522X

Publication Date December 30, 2020
Acceptance Date December 7, 2020
Published in Issue Year 2020

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