Finding the solutions of simultaneous nonlinear equations

For finding multiple solutions of simultaneous nonlinear equations, the paper presents a homotopy method, based on integrating a regular differential equations. This differential system is solved by a predictor-corrector scheme, based on Hermite corrector formula; and the approximate solutions of the system of nonlinear equations is obtained. Then, with the approximate solutions as initial points, the method of Newton-Raphson gives multiple solutions of the system of nonlinear equations.