The main interest is the numerical treatment of boundary value problems of the second and fourth order
with their equivalent Fredholm integral equation forms. Comparison of the performance of the SOR and the KSOR
methods on the systems arise from the differential form and those arise from the equivalent Fredholm form by using
discretization techniques of the same accuracy are considered. It is found that the SOR and the KSOR use the same
number of iterations with the same system but with different relaxation factors. The number of iterations in case of
the integral representations is approximately less than quarter the number of iterations in case of the differential
representations in the same time the computational work per iteration in the differential form (sparse systems) is less
than that of the integral form. We discussed the advantages of using the integral representation over the use of the
differential representation especially when we have a good approximation of the relaxation parameters. All
calculations are done with the help of computer algebra system (MATHEMATICA 8.0). |
