Some Iterative Methods For Solving System Of Nonlinear Equations

With the development of science and technology, numerical calculation plays a vital role inscience research and engineering technology, and numerical solution method for nonlinearequations, an important research in mathematical calculation, plays an important role in variousfields. This paper mainly discusses iterative methods for the solution of nonlinear equations. Thefull text is divided into four chapters.The first chapter gives some related definitions and notation used in this paper with anintroduction of the research background and research situation at home and abroad.The second chapter summarizes some commonly used iterative methods for the solution ofnonlinear equations. The first part introduces the classical Newton iterative method with theprominent advantage of its convergence speed, and the disadvantage of its large derivativecalculation when f(x) is complex as a result of the need to provide value for each iteration. Thesecond part introduces two iterative methods of the fourth order for solutions of nonlinearequations. The third part introduces two three-step iterative methods for systems of nonlinearequations.The third chapter presents, on the basis of three-step iterative method of the fifth order for thesolution of nonlinear equations, and according to the quadrature formula, a new iterative method,that is four-step iterative method of the eighth order for solution of nonlinear equations with prooffor the eighth convergence order of the solution and numerical examples for its effectiveness.The fourth chapter gives a summary of current research and prediction of next research.