Method for determining relaxation factor for modified Newton-Raphson method

In order to reduce the CPU time for the modified Newton-Raphson method which introduces a relaxation factor, the effect of the relaxation factor on the residual of the Galerkin method is examined in detail. It is shown that a relaxation factor, which always provides convergent solutions, can be easily searched for. Various methods for searching for the relaxation factor to be used are compared with each other.