The Research Of Iterative Method For Solving Nonlinear Equation

Following the development in science and the applying ofcomputers, the solution of nonlinear equation is the most important andchallenge problem in science and engineer. Especially, some keyquestions in engineering calculation of recent physics and science aredepended on the solution of nonlinear equation, nonlinear problem playa great role in modern scientific computing disciplines.Many equationsderived from practical problem are always the nonlinear forms. Since,the solution of nonlinear equation has been the core of studies ofnumerical workers.The iterative method is an excellent method to solvenonlinear operator equations f (x)=0in Banach space. Whether thenonlinear problems will be solved well or not is directly affected by thechoice of iterative methods. For the past several decades, the research of iterative methods became the hardcore of finding solution to all kinds ofthe nonlinear problems. Therefore, the research on iterative methodmeans a lot in terms of scientific research and practical application. Forthe past several decades, the rapid advancement of scientific Technologyand computers has effectively promoted the research of nonlinearproblems. Strictly examined by practice, some classical methods areproved to have some drawbacks. For example, some iterative methodhas higher order of convergence but low computational efficiency or loworder of convergence but higher computational efficiency. Especially inlarge scale Calculation, the computational efficiency plays a crucial role,which calls on us to avoid applying computational methods with lowcomputational efficiency. Thus, when considering the convergence orderof computational method, we also take computational efficiency intoconsideration particularly. The key of our research is to find thecomputational methods with higher convergence order and highercomputational efficiency. Therefore, the research on iterative methodwith high computational efficiency means a lot in terms of both scientific research and practical application.Two works were studied in this dissertation: One is to improve theComputational efficiency by improving the know iterative methods, theother is that two New third-order convergence methods of solvingnonlinear equation are developed by the Padé approximation theory,Order of convergence of the new iterative methods is proved.