A Differentiate Continuation Method Along Vector Field Line For Solving Higher-Dimensional Nonlinear System Equations

In the mathematics field,solving system of nonlinear equations is an important problem.The traditional methods include Newton's method,Extension method and some others.Newton's method,Extension method have fast convergence property,put they often tail to solve some nonlinear system equations because their convergence is strongly related to the initial point.Based on the comparison of Newton's method and Extension method, A differentiate continuation method along vector field line for solving higherdimensional nonlinear system equations is proposed.It is not related to the initial point,It is finished along vector field.we have proved it.Three example were given to demonstrate the feasibility of the numerical method,and validated our theoretical findings.And a usual algorithms was given for solving higher-dimensional nonlinear system equations.