On preconditioned iterative methods for Burgers equations. (English) Zbl 1144.65034
Authors’ summary: We study the Newton method and a fixed-point method for solving the system of nonlinear equations arising from the Sinc-Galerkin discretization of the Burgers equations. In each step of the Newton method or the fixed-point method, a structured subsystem of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear subsystems. The bounds for eigenvalues of the preconditioned matrices are derived and numerical examples are given to illustrate the effectiveness of the proposed methods. We also find that a combination of the Newton/fixed-point iteration with the preconditioned generalized minimal residual (GMRES) method is quite efficient for the Sinc-Galerkin discretization of the Burgers equations.
Reviewer: B. Döring (Düsseldorf)
MSC:
65H10 | Numerical computation of solutions to systems of equations |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
35Q53 | KdV equations (Korteweg-de Vries equations) |
65F35 | Numerical computation of matrix norms, conditioning, scaling |