Two-grid method for the stationary Burgers equation

Abstract

Abstract A two-grid method is investigated for solving the boundary value problem for nonlinear ordinary differential equation of the second order with a small parameter at the highest derivative. The solution to the problem has large gradients in the boundary layer region. The application of the central difference scheme on the Shishkin and Bakhvalov grids is investigated. Previously, this scheme was investigated only in the case of a linear equation. It is shown that in the case of the considered nonlinear problem, this scheme on the Shishkin and Bakhvalov grids has a convergence uniform in a small parameter. On the basis of computational experiments, it is shown that the use of the two-grid method leads to a reduction in computational costs when implementing the difference scheme. It is shown that in the two-grid method it is effective to apply the Richardson method to improve the accuracy of the difference scheme.