On the convergence of the method of iterative approximate factorization of difference operators of high-order accurate bicompact scheme for nonstationary three-dimensional hyperbolic equations

The convergence of the iterative approximate factorization method for operators of the bicompact scheme for numerical solution of hyperbolic equations is investigated. In this method, iterations are made in order to eliminate the approximate factorization error from the numerical solution. Iterations convergence is studied in case of the bicompact scheme of fourth order in space for the non-stationary three-dimensional linear advection equation with constant positive coefficients. It is proved that iterations converge for all positive Courant numbers in all three space dimensions. A theoretical estimate for convergence rate of iterations is obtained. This estimate is confirmed in a numerical experiment for different relations between Courant numbers.