Study On Iterative Algorithm Of Nonlinear Equations

Following the science and technology and the applying of computers, we will have avery important and challenging problem in the field of science and engineer. That is theproblem of solving nonlinear equations. Not just in the mathematical field, otherdisciplines will also encounter such problems. For example: circuit issues of thephysical aspects, economic and nonlinear programming problems, and so on. It can besummed up as a mathematical model, namely, solving the nonlinear equations. To solvethe nonlinear equation of the root of the solution has a lot of kinds, and the Newtoniteration method is the most classic and basic method. If we select the appropriateiteration method, we can get better computation efficiency and convergence speed. Thus,the study of iterative method has very important value and significance of reality. Basedon the study of the iteration algorithm of nonlinear equations, this paper presents a newiterative method for nonlinear equations, proved that the convergence order of themethod is fifteen order, and the new algorithm is compared with the existing algorithmthrough numerical in this paper.This paper is divided into four parts: the first part mainly introduces the backgroundand present situation about solving nonlinear equation problems. The second partintroduces several important methods of solving nonlinear equations. The third part, weproposed one new iterative format on the basis of the Newton iteration method.Numerical experiments show that this method has some advantages. Finally, oursolution for nonlinear equations is summarized and prospected.