Buckling of string in vertical well can summed up a non-linear equation,of which Mitchell gave the new exact solutions in 2002.

Each parameter of helix is extracted by numeric solution of the non-linear equation.

In this paper,a new convergence theorem and error estimate for some new modifications of Newton\'s method are obtained by means of Newton\'s theorem,under the foundations of Newton\'s method for solving non-linear equation.

Convergence of numerical methods for the nonlinear equation in chemical reaction engineering;

Newton-like methods for solving nonlinear equations;

Population Migration Algorithm for Solving Nonlinear Equation;

Application individual independent optimization evolutionary strategies to solve approximate solutions of nonlinear equations;

Applications of nonlinear equations in several computing problems;

A new high accuracy iteration method for solving nonlinear equations;

The pro- posed method can be applied to notonly weakly non-linear equations,butalso strongly ones.

A Weights Coupling neural network is proposed, and the possibility of solving non linear equations with it is discussed.

Applying Gauss theorem, a non linear equation is given a calculation, which is characterized by three electric lines having the same density of electric charges as that in the static field, being parallel and of infinite length, and by uniform distribution of linear charges near the terminal point as well.

In the paper, a new method,the weighed average method,is put forward to resolve the approximate analytic solution of non linear equation with clearance system.