On the Convergence of Iterative Methods for Linear Systems arising from Singularly Perturbed Equations.

Paul A. Farrell

Department of Mathematics & Computer Science, Kent State University, Kent, OH 44242, U.S.A.


Singularly perturbed differential equations are models for convection dominated flow problems. Many numerical methods for such differential equations, particularly those which seek convergence uniformly in the perturbation parameter, utilize some form of fitting or upwinding of the operator. In such cases, the matrices arising may be highly non-symmetric. Previous studies have shown that, when using Gauss-Seidel type iterations, it is crucial to sweep the mesh in the direction of the underlying flow. In this paper, we will examine iterative methods for singularly perturbed equations further, particularly from the perspective of maintaining uniform in the perturbation parameter convergence.