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1 2015

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On an application of an interval backward ﬁnite diﬀerence method for solving the one-dimensional heat conduction problem

Jankowska M., Marciniak A., Hoﬀmann T.

Control and Cybernetics

2015

Vol. 44, no. 4

463--480

The paper concerns the interval method for solving the one-dimensional heat conduction problem. It is based on the conventional backward ﬁnite diﬀerence scheme with the appropriate local truncation error terms that are also taken into account. For the theoretical formulation of the interval approach we can show that the exact solution is included in the interval one. In practice, there are problems, for which we cannot determine the endpoints of the error term intervals exactly. Nevertheless, if we use the appropriate approximation, related to the endpoints considered, then the numerical experiments conﬁrm that the interval solution includes the exact one.