×

zbMATH — the first resource for mathematics

On high-order compact difference schemes. (English) Zbl 0951.65104
Fourth-order schemes with three-point stencils in each spatial directions for 2D and 3D variable coefficients convection-diffusion equations are described. It is shown that under certain conditions the matrices of the relevant linear systems are monotonic. As a particular case, the Poisson equation in polar coordinates is considered. The schemes are generalized to unsteady initial-boundary value problems for parabolic equations. The presented error estimates show the fourth-order solution mesh-convergence in the case of steady-state problems, unsteady solutions being of the first order in time and the fourth order in space.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI