course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Numerical Analysis |
II |
77 |
|
A2.19 B2.20 |
2004 |
(i) The five-point equations, which are obtained when the Poisson equation
where
Formulate the Gauss-Seidel method for the above linear system and prove its convergence. In the proof you should carefully state any theorems you use. [You may use Part (ii) of this question.]
(ii) By arranging the two-dimensional arrays $\left{u_{m, n}\right}{m, n=1, \ldots, M}$ and $\left{b{m, n}\right}_{m, n=1, \ldots, M}$ into the column vectors