Isomorphic iterative methods in solving singularly perturbed elliptic difference equations

A new approach for the efficient numerical solution of Singular Perturbation (SP) second order boundary-value problems based on Gradient-type methods is introduced. Isomorphic implicit iterative schemes in conjuction with the Extended to the Limit sparse factorization procedures [9] are used for solving SP second order elliptic equations in two and three-space dimensions. Theoretical results on the convergence rate of these first-degree iterative methods for three-space variables are presented. The application of the new methods on characteristic SP boundary-value problems is discussed and numerical results are given.