TY  - JOUR
T1  - On The Stability of Nonlocal Boundary Value Problem for Schrödinger-Parabolic Equations
AU  - Ozdemir, Yildirim
PY  - 2020
DA  - December
Y2  - 2020
DO  - 10.47086/pims.778004
JF  - Proceedings of International Mathematical Sciences
JO  - PIMS
PB  - İbrahim ÇANAK
WT  - DergiPark
SN  - 2717-6355
SP  - 90
EP  - 95
VL  - 2
IS  - 2
LA  - en
AB  - 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.
KW  - Partial differential equations
KW  - Nonlocal boundary value problem
KW  - Stability
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [4] A. Ashyralyev, Nonlocal boundary-value problems or abstract parabolic equations: wellposedness in Bochner spaces, J. Evol. Equ., 6 (2006), 1-28.
CR  - [5] A. Ashyralyev, and Y. Ozdemir, On nonlocal boundary value problems hyperbolic-parabolic equations Taiwan. J. Math., 4 (2007), 1075-1089.
CR  - [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.
CR  - [7] A. Ashyralyev, and A. Sirma, Nonlocal boundary value problems for Shrödinger equations, Comput. Math. Appl., 55 (2008), 392-407.
CR  - [8] A. Ashyralyev, and B. Hicdurmaz, A note on the fractional Schrödinger differential equatios, Kybernetes, 40 (2011), 736-750.
CR  - [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.
CR  - [10] Y. Ozdemir, and M. Kucukunal, A note on nonlocal boundary value problems for hyperbolic Schrödinger equations, Abstr. Appl. Anal., 2012 (2012), 1-12.
CR  - [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.
CR  - [12] A. A. Samarskii, and E. S. Nikolaev, Numerical Methods for Grid Equations, Vol. 2 Iterative Methods, Birk¨auser, Basel, 1989.
UR  - https://doi.org/10.47086/pims.778004
L1  - https://dergipark.org.tr/en/download/article-file/1231191
ER  -