
40 Programming for Chemical Engineers
These values are then substituted back on the right-hand side of the equation,
giving another set of values of x. We repeat the process until the values obtained
are almost equal to the previous values.
Both the Jacobi and Gauss-Seidel methods have similar processes except
that in the Gauss-Seidel method, the new values of the unknowns are inserted
into the next equation as they are generated. In this way, the method requires
less iteration than the Jacobi method.
Let’s proceed with an example.
Example Problem 2.3. Given the same linear equations, determine the values
of x
1
, x
2,
and x
3
using the Gauss-Seidel ...