An interval backward finite difference method for solving the diffusion equation with the position dependent diffusion coefficient
[ 1 ] Instytut Mechaniki Stosowanej, Wydział Budowy Maszyn i Zarządzania, Politechnika Poznańska | [ P ] employee
2012
paper
english
- one-dimensional diffusion equation
- position dependent diffusion coefficient
- backward finite difference method
- interval methods
EN The paper deals with the interval backward finite difference method for solving the one-dimensional diffusion equation with the position dependent diffusion coefficient and the boundary conditions of the first type. The interval method considered is based on the conventional backward finite difference method. Moreover, it takes into account a formula of a local truncation error of the method. Such local truncation error of the conventional method is bounded by the appropriate interval values. In most scientific applications we cannot find the endpoints of such intervals exactly and it is of great importance to approximate them in the most accurate way. The paper presents a method of such approximation.
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