Iterative approximate factorization of difference operators of high-order accurate bicompact schemes for multidimensional nonhomogeneous quasilinear hyperbolic systems

For solving equations of multidimensional bicompact schemes, an iterative method based on approximate factorization of their difference operators is proposed. The method is constructed in the general case of systems of two- and three-dimensional quasilinear nonhomogeneous hyperbolic equations. The unconditional convergence of the method is proved as applied to the two-dimensional scalar linear advection equation with a source term depending only on time and space variables. By computing test problems, it is shown that the new iterative method performs much faster than Newton’s method and preserves a high order of accuracy.