Open AccessTwo-grid method for the stationary Burgers equation
Author(s) -
Н. А. Задорин,
S B Shagaev
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1791/1/012090
Subject(s) - mathematics , grid , nonlinear system , finite difference method , ordinary differential equation , boundary value problem , convergence (economics) , burgers' equation , mathematical analysis , central differencing scheme , partial differential equation , scheme (mathematics) , finite difference , basis function , differential equation , finite difference coefficient , geometry , finite element method , physics , quantum mechanics , mixed finite element method , economic growth , economics , thermodynamics
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.