The evaluation of can be accomplished in the following ways:

(a) Vertical Sweep Upwards may be written in a pseudo FORTRAN code as

DO 10     J = 2, M – 1

DO 10     I = 2, L – 1

10

Here is the currently available value in storage and all the coefficients including are known. For each we shall get a system of equations if we substitute In order words, for each a tridiagonal matrix is available which can be solved for all row of points at that Once one complete row is evaluated for any particular the next will be taken up, and so on.

(b) Horizontal Sweep Forward may be written in pseudo FORTRAN code as

DO 20     I = 2, L – 1

DO 20     J = 2, M – 1
20

Again is the currently available value in storage from previous calculations. For each , we get a system of equation if we substitute A tridiagonal matrix is available for each . Once one complete column of points are evaluated for any particular the next will be taken up, and so on. The vertical sweep upward and downward are repeated. Similarly the horizontal sweep forward and rearward are also repeated until convergence is achieved. For solving tridiagonal system, the tridiagonal matrix algorithm (TDMAS) due to Thomas (1949) is deployed. The above mentioned evaluation procedure is known as line-byline TDMA.

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