For the H-nonlinear equation systems produced by stiff nonlinear function f(y): y ∈ Rm→Rm, the paper presents a new Newton-like iterative so- lution method: completely-square method, establishes its convergence theory and offers four simple algorithms for approximate calculation of optimum iterative pa- rameter in this method. The iterative method do not need to compute(f’)2, and LU-decomposition only need to be done for some m × m matrix. Numerical examples show that if appropriate approximate optimum iterative parameter is selected on the coefficients in the hybrid method that products the H-nonlinear equation systems then the iterative solution method in the paper is high efficiency.
