Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations

Abstract

Summary:The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solved