Convergence and Accuracy of the Method of Iterative Approximate Factorization of Operators in Multidimensional High-Accuracy Bicompact Schemes

Abstract

The convergence and accuracy of a method for solving high-order accurate bicompact schemes having the fourth order of approximation in spatial variables on a 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 the second) order of accuracy of bicompact schemes in time. The convergence of these iterations for both two- and three-dimensional bicompact schemes as applied to the linear inhomogeneous advection equation with positive constant coefficients is proved using the spectral method. The efficiency of two parallel algorithms for solving equations of multidimensional bicompact schemes is compared. One of them is the spatial marching algorithm for calculating unfactorized schemes, and the other is based on iterative approximate factorization of difference operators of the schemes.