A new numerical method of nonlinear equations by four order Runge-Kutta method

In this paper, we use homotopy method to transfer nonlinear equations to a differential equations, then we apply four-order Runge-Kutta method to solve the differential equations for getting a more stable and easily convergent solution. What is more important, we demonstrate a complete proof of the whole process, which provide a scientific foundation for the method as a whole. In the end, we give a specific example that is solved by the approach we have proved, which shows the efficiency and stability of the method. With the new methods, some certain nonlinear equations can be simply and precisely caculated, which can contribute to production planning and control or operation problems significantly.