The Iterative Methods To Solve Systems Of Nonlinear Equations

In recent decades,With the rapid development of computer,the numericalanalysis research has vigorously promoted,many theoretical and practicalproblems(physics,engineering technology,nonlinear mathematics) can be classifiedas some specific problems for solving nonlinear equations.Therefore,nonlinearequations problem is becoming important research topics in the field of numericalcalculation.This thesis is focused on some improved Newton methods for solvingnonlinear equations.The contents of this thesis can be summarized as follows:In Chapter1, we give a brief introduction to the concepts, theorems and thestate of the art of iterative methods for solving nonlinear equations,then weintroduce in detail of Newton iterative method and the further study on it.In Chapter2, we mainly summarize some iterative method with three-orderconvergence:firstly we give several well known iterative methods are introducedfor solving nonlinear equations, including Chebyshev iterative method, Halleyiterative method, Super-Halley iterative method and its deformation. Secondly, weintroduce the Adomian decomposition method,and give some iterative methodswith three-order convergence which are based on this decomposition method,thenwe prove the order of convergence.Thirdly,we discuss a series of iterative formulaswith three-order convergence which are based on numerical quadrature formulasfor solving nonlinear equations.In Chapter3,by using the third-order convergence iterative scheme based onthe previous chapter reassemble with the four-order convergec iterative method,weget two new method of iteration.Through the proof we can see that the new methodshave six order convergence.At last, we give some numerical examples to show theeffectiveness of the two new methods.In Chapter4,Take the summary of this thesis:we give some ideas to improvethe Newton’s method and show the prospect of it’s future.