Numerical Solution of NBV Problem for Elliptic Differential Equations: Bitsadze-Samarkii Type Elliptic Equations - Tapa blanda

Bitsadze-Samarskii nonlocal boundary value problem for elliptic differential equation in a Hilbert space H with the self-adjoint positive definite operators A is considered. The well-posedness of this problem in Hölder spaces with a weight is established. The coercivity inequalities for the solutions of the nonlocal boundary value problem for elliptic equation are obtained. The second and fourth orders of accuracy difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability estimates, coercivity and almost coercivity inequalities for the solution of these difference schemes are established. The well-posedness of these difference schemes in Hölder spaces with a weight is proved. The Matlab implementation of these difference schemes for elliptic equation is presented. The theoretical statements for the solution of these difference schemes are supported by the results of numerical examples.

Elif Oztürk was born in Bursa, Turkey in 1984. She took her Bachelor degree from Yıldız Technical University. She graduated from Departments of Mathematics and Statistics in 2006. She took the degree of Master of Applied Mathematics from Fatih University in 2008. She is Phd candidate at Uludag University.