A practical choice of parameters in improved SOR-Newton method with orderings

In this paper, on the basis of the results of Ishihara et al. (1997), we first discuss global convergence theorems for the improved SOR-Newton and block SOR-Newton methods with orderings applied to a system of mildly nonlinear equations, which includes as a special case the discretized version of the Dirichlet problem, for the equation ϵΔu + p(x)ux + q(y)uy = f(x, y, u), where f is continuously differentiable and fu(x, y, u) ⩾ 0. Moreover, we propose a practical choice of the multiple relaxation parameters {ωi} for them. Numerical examples are also given.