A central-backward difference interval method for solving the wave equation

Authors:
Andrzej Marciniak;Barbara Szyszka
Affiliations:
Institute of Computing Science, Poznan University of Technology, Poznan, Poland;Institute of Mathematics, Poznan University of Technology, Poznan, Poland
Venue:
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Year:
2012

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Abstract

The paper is devoted to an interval difference method for solving one dimensional wave equation with the initial-boundary value problem. The method is an adaptation of the well-known central and backward difference methods with respect to discretization errors of the methods. The approximation of an initial condition is derived on the basis of expansion of a third-degree Taylor polynomial. The initial condition is also written in the interval form with respect to a discretization error. Therefore, the presented interval method includes all approximation errors (of the wave equation and the initial condition). The floating-point interval arithmetic is used. It allows to obtain interval solutions which contain all calculations errors. Moreover, it is indicated that an exact solution belongs to the interval solution obtained.