An interval backward finite difference method for solving the diffusion equation with the position dependent diffusion coefficient

Authors:
Malgorzata A. Jankowska
Affiliations:
Institute of Applied Mechanics, Poznan University of Technology, Poznan, Poland
Venue:
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
Year:
2011

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Abstract

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.