Title
Numerical Solution of NBV Problem for Elliptic Differential Equations: BitsadzeSamarkii Type Elliptic Equations,Used
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BitsadzeSamarskii nonlocal boundary value problem for elliptic differential equation in a Hilbert space H with the selfadjoint positive definite operators A is considered. The wellposedness of this problem in Hlder 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 wellposedness of these difference schemes in Hlder 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.
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