We considered Poisson differential equation with Dirichlet boundary conditions and one nonlocal boundary condition. Finite-difference scheme was investigated for this problem. The eigenvalues of such problem depend on few parameters in the nonlocal boundary condition. The convergence rate for Cheby-shev iterations depends on the number of the discrete mesh points. The convergence is more faster when the maximal eigenvalue of the corresponding nonsimmetric matrix is simple.
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