Well-posedness of Bitsadze-Samarskii problem for elliptic differential and difference equations

Speaker: Dr. Fatma Songul Ozesenli Tetikoglu

Abstract: The Bitsadze-Samarskii nonlocal boundary value problem
-u”(t) + A u(t) = f(t), u'(0)=a, u'(1)=b u'(c) + d
for the elliptic differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for solutions of the nonlocal boundary value problem for the elliptic equation are obtained. The first, second, third 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 solutions of these difference schemes are established. The Matlab implementations of these difference schemes for the elliptic equation are presented. The theoretical statements for the solutions of these difference schemes are supported by the results of numerical examples.