The resulting system of linear algebraic equations is not tridiagonal because of the five unknowns and In order to examine this further, let us rewrite Eq. (5.7) as

(5.9)

where

Figure 5.2: Two-dimensional grid on the ( ) plane.

Eq. (5.9) can be applied to the two-dimensional (6×6) computational grid shown in Fig. 5.2.

A system of 16 linear algebraic equations have to be solved at time level, in order to get the temperature distribution inside the domain. The matrix equation will be as the following:

(5.9)

where

The system of equations, described by Eq. (5.9) requires substantially more computer time as compared to a tridiagonal system. The equations of this type are usually solved by iterative methods. These methods will be described in a subsequent lecture. The quantity is the boundary value.

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