Abstract: This paper discusses how to f
ind the global set of solutions to two types of systems of nonlinear equations f
requently encountered in mechanical engineering. One type is the system of nonli
near polynomial equations, and a numerical approach using the homotopy method is
presented to work out all the complex or real solutions to the polynomial syste
ms without initial value selection. The other type is the system of transcendent
al equations with trigonometric functions, and a numerical method based on Newto
n’s iterative method is proposed, which can find all the real roots of the syst
em of transcendental equations with trigonometric functions without initial valu
e selection in the specified intervals. Numerical examples are given to confirm
the validity of the numerical methods. The presented methods are ultraconvenient
because there is no initial value selection in the root-finding procedure and
can easily be implemented with computers.

Key words: system of nonlinear polynomial equations, homotopy method, system of transcendental equations with trigonometric functions, numerical method, global set of solutions