Chebyshev iteration for the problem with nonlocal boundary condition

Abstract

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.