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

Yıl 2020, Cilt: 2 Sayı: 2, 90 - 95, 30.12.2020

Yildirim Ozdemir

https://doi.org/10.47086/pims.778004

Öz

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.

Anahtar Kelimeler

Partial differential equations, Nonlocal boundary value problem, Stability

Kaynakça

• [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.