Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation

This paper presents an efficient algorithm for solving a nonlinear equation. In our algorithm, the nonlinear system f (x) = 0 is solved by a homotopy method, in which a homotopy H (x,t) = f (x)-(1-t) f (x0) is introduced and the solution path of H(x, t) = 0 is followed from an obvious solution (x0,0)to the solution (x*,1) which we seek. An ordinary differential equation based on Newton homotopy is used for following the solution path. Our homotop algorithm is much more efficient than the conventional iterations type algorithms. Some numerical examples are given in order to demonstrate the effectiveness