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Error estimation for the diffusion equation solution based on the schemes with weights

A. I. Sukhinov, A. E. Chistyakov, A. V. Shishenya

Taganrog Institute of Technology of the South Federal University

Abstract: In applied problems it is often necessary to solve diffusion equation. The most efficient methods for solving such types of problems are grid methods that, nevertheless, have an approximation error. In the given paper a linear diffusion equation with variable coefficients is considered, for which estimation for error of approximation by scheme with weights is obtained. A method for the calculation of the optimal weight, which provides a minimum error for the given value of the grid spacing, is developed.

Keywords: diffusion equation; schemes with weights; approximation error.

UDC: 519.6

Received: 18.06.2012

 English version: Mathematical Models and Computer Simulations, 2014, 6:3, 324–331

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