The variation-difference scheme of solution of Dirichlet’s problem for elliptic pseudodifferential equations of second order

The variation-difference scheme of the solution of Dirichlet’s problem is presented for the equation $Au+Bu=f$, where $A$ is an elliptic operator of the second order and $B$ is pseudodifferential operator arised by the symbol $b(\xi)$, satisfying the estimation $b(\xi)\leq C|\xi|, C >0$. It has been proved that the resulting scheme has first order convergence. In addition it has been established that the condition number of the resulting matrix has $O(h^{-2})$ order.