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January  2007, 7(1): 29-51. doi: 10.3934/dcdsb.2007.7.29

Well-posedness of the modified Crank-Nicholson difference schemes in Bochner spaces

Allaberen Ashyralyev 1,

1. 

Department of Mathematics, Fatih University, 34500, Buyukcekmece, Istanbul, Turkey

Received  January 2006 Revised  June 2006 Published  October 2006

The nonlocal boundary value problem $v$’$(t)+Av(t)=f(t)(0\leq t\leq 1),v(0)=v(\lambda )+\mu ,0<\lambda \leq 1$ for differential equations in an arbitrary Banach space $E$ with the strongly positive operator $A$ is considered. The well-posedness of the modified Crank-Nicholson difference schemes of the second order of accuracy for the approximate solutions of this problem in Bochner spaces is established. In applications, the almost coercive stability and the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problem for parabolic equation are obtained.
Keywords: modified Crank-Nicholson difference schemes., well-posedness, coercivity inequalities, Banach spaces, Abstract parabolic problem.
Mathematics Subject Classification: Primary: 65 N, 47 D; Secondary: 34 .
Citation: Allaberen Ashyralyev. Well-posedness of the modified Crank-Nicholson difference schemes in Bochner spaces. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 29-51. doi: 10.3934/dcdsb.2007.7.29
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