Compact difference schemes for elliptic equations with mixed derivatives on arbitrary grids
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V.I. Paasonen
Abstract
- We study difference schemes with indefinite coefficients and indefinite right-hand sides on stencils that consist of any number of arbitrarily located points. In the two-dimensional case we obtain linear systems of equations for the calculation of coefficients in ordinary (noncompact) and compact schemes and conditions on the right-hand side under which the approximation order of differential equations would be equal to a predetrmined natural number. Analogously we study the behaviour of ordinary and compact approximations of universal boundary conditions, including the conditions of the first, second, and third kinds. In the three-dimensional case we establish the number of conditions which specify coefficients and the right-hand sides of schemes. We consider particular examples of schemes in the plane and in the space.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Contents
- Momentumless turblent wake dynamics in a linearly stratified medium. The results of numerical experiments
- Far plane turbulent wake dynamics
- Numerical simulation of the interaction of a solitary wave with a partially immersed body
- Splitting algorithms in the finite volume method
- Analysis of quality of numerical grids produced by a comprehensive grid generator
- Compact difference schemes for elliptic equations with mixed derivatives on arbitrary grids
Articles in the same Issue
- Contents
- Momentumless turblent wake dynamics in a linearly stratified medium. The results of numerical experiments
- Far plane turbulent wake dynamics
- Numerical simulation of the interaction of a solitary wave with a partially immersed body
- Splitting algorithms in the finite volume method
- Analysis of quality of numerical grids produced by a comprehensive grid generator
- Compact difference schemes for elliptic equations with mixed derivatives on arbitrary grids
