The Iterative Methods To Solve Systems Of Nonlinear Equations

With the development of science and technology, as well as the wideapplications of electronic information technology, nonlinear problems arebecoming important research topics in the field of computational mathematics,where the solution of system of nonlinear equations is the most basic problem. Thisthesis is focused on some iterative methods for solving the system of nonlinearequations.The main contents of this thesis are outlined as follows:In Chapter1, we give a brief introduction to the basic notations, concepts andthe state of the art of iterative methods for solving the system of nonlinearequations,In Chapter2, firstly several well known iterative methods are introduced forsolving the system of nonlinear equations, including Newton iterative method,Chebyshev iterative method and Halley iterative method. Secondly, we discuss aseries of iterative formulas which are based on numerical quadrature formulas forsolving system of nonlinear equations. Thirdly, we introduce the Adomiandecomposition method, and give some iterative methods for solving the system ofnonlinear equations which are based on this decomposition method.In Chapter3, the two new iterative methods for solving system of nonlinearequations with higher convergence are given. First, by using the third-orderconvergent iterative scheme based on the Adomian decomposition method toreassemble with the iterative method obtained by the quadrature formulas, we getthe first class of iterative methods with forth-order convergence. Second, bycombining the iterative schemes based on the Adomian decomposition method withthe iterative methods obtained by the quadrature formulas in a weighted way, weget the second class of iterative methods. At last, we give some numerical examplesto show the effectiveness of the two new methods.In Chapter4, we give the summary of the thesis and some ideas of what can bedone in the future.