About the convergence and accuracy of the method of iterative approximate factorization of operators of multidimensional high-accuracy bicompact schemes

In the work, the convergence and accuracy of the method of solving high-precision bicompact schemes having the fourth order of approximation in spatial variables on the minimum stencil for a multidimensional inhomogeneous advection equation are investigated. The method is based on the approximate factorization of difference operators of multidimensional bicompact schemes. In addition, it uses iterations to preserve a high (higher than second) order of accuracy of bicompact schemes in time. Using the spectral method, we were able to prove the convergence of these iterations for both twodimensional and three-dimensional bicompact schemes for a linear inhomogeneous advection equation with constant positive coefficients. The effectiveness of two parallel algorithms for solving multidimensional bicompact schemes equations is compared. The first of them is the spatial marching algorithm for calculation of non-factorized schemes, and the second is based on an iterative approximate factorization of difference operators of the schemes.