On a difference scheme of fourth order of accuracy for the Bitsadze-Samarskii type nonlocal boundary value problem
No Thumbnail Available
Date
2012-07-26
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Abstract
The BitsadzeSamarskii type nonlocal boundary value problem d2u(t)dt2+Au(t)=f(t),0H is considered. Here, f(t) be a given abstract continuous function defined on [0,1] with values in H, phi and be the elements of D(A), and j are the numbers from the set [0,1]. The well-posedness of the problem in Holder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The fourth order of accuracy difference scheme for approximate solution of the problem is presented. The well-posedness of this difference scheme in difference analogue of Holder spaces is established. For applications, the stability, the almost coercivity, and the coercivity estimates for the solutions of difference schemes for elliptic equations are obtained.
Description
Keywords
Mathematics, Elliptic equation, Bitsadze-Samarskii nonlocal boundary value problem, Difference scheme, Stability, Well-posedness, Elliptic-equations, Spaces, Coercive force, Convergence of numerical methods, Applied science, Approximate solution, Continuous functions, Difference schemes, Elliptic equations, Mathematical method, Nonlocal boundary-value problems, Positive definite, Boundary value problems
Citation
Ashyralyev, A. ve Öztürk, E. (2013). "On a difference scheme of fourth order of accuracy for the Bitsadze-Samarskii type nonlocal boundary value problem". Mathematical Methods in the Applied Sciences, 36(8), 936-955.