Interval Finite Difference Method for Solving the One-Dimensional Heat Conduction Problem with Heat Sources

The one-dimensional heat conduction equation with the term concerning some heat sources, together with the mixed boundary conditions is considered. Such problems occur in the area of the bioheat transfer and their well-known example is given by the Pennes equation. The paper deals with some interval finite difference method based on the Crank-Nicolson finite difference scheme. In the approach presented, the local truncation error of the conventional method is bounded by some interval values. A method of approximation of such error term intervals is also presented.

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