The Alternate-Triangular Method

Abstract

In this chapter we study the alternate-triangular iterative method* for solving an operator equation with a self-adjoint operator. In Section 10.1 the general theory of the method is laid out, described by the construction of the iterative scheme and by indicating the set of iterative parameters. The method is illustrated on a sample problem — a Dirichlet difference problem for Poisson’s equation in a rectangle. In Section 10.2 this method is applied to the solution of elliptic difference equations with variable coefficients and mixed derivatives in a rectangle. A variant of the alternate-triangular method is constructed in Section 10.3 to solve an elliptic equation with variable coefficients on a non-uniform grid in a arbitrary region.