The Research Of Nonlinear Equation Iterative Method

In the study of social problems and natural phenomena mathematics is a tool, so alot of problems in the engineering and technology can be attributed to the root of thenonlinear equation to solve the problem. For such a problem, especially more than fourequations f (x)=0,we generally can use the analytic method to find out its exact solutionor can’t use the coefficient to represent its root, and then we can only find some numericalmethod to calculate the approximate solution. At present, in addition to the classic method,researchers continue to put forward many new methods, for example, paper [1][13][14],this paper provides several new methods for solving non-linear equations, they haveenriched the content of the root of the nonlinear equation. This article is mainly based onNewtonian iteration function, Newton’s method for the single function and a new iterativefunction, given its iterative format, prove its convergence section number, and further studyits convergence and convergence efficiency index.This paper is mainly divided into five parts. The first part introduces the backgroundof iterative method. The second part mainly introduces some commonly used to solvenonlinear equation method. The third part mainly introduces a modified Newton iterationmethod. The fourth part mainly introduces the Newton-Cotes method for solving non-linearequations. The fifth part is the full text of the summary and prospect.