On the behavior of the error in numerical iterative method for PDE

Abstract

The purpose of paper is to analyze the behavior of the error in the iterative method. Especially, we are interested in the classical iterative method such as SOR method and its preconditioning techniques to solve the linear system Au= q. In order to accelerate convergence, many researchers proposed several preconditioners [4–8]. There is also preconditioner available for both classical iterative and Krylov subspace methods. We focus on the behavior of error to find a good preconditioner. We treat difference equation derived from partial differential equation(PDE), because the coefficient matrix given by using difference approximation is easy to investigate. By examining the behavior of the error, we choose an effective preconditioner, and show the numerical results.