The Convergence Of Numerical Methods For Solving Nonlinear Equations

With the rapid development of science and technology and the widespread popular-ity of computer application,solving the nonlinear operator equations is widely used in economy,physics,information science,the field of life science,computer science and so on.This paper mainly studies the convergence of numerical methods for solving nonlinear operator equations.In Chapter 1,we introduce the development of numerical methods for solving general nonlinear operator equations F(x)=0 and the relevant preliminary knowledge such as order of convergence,convergence condition,divided difference and the related conclusions in Banach spaces.In Chapter 2,we studies the convergence problem of the Ulm-like method for solving the general nonlinear operator equations F(x)= 0 which avoids computing(approximate)Jacobian matrices and solving(approximate)Jacobian equations.In this section,we established the local convergence result and proved the super-linear convergence property of the Ulm-like rmethod.Moreover,numerical experiments are given in the last section to illustrate our results.In Chapter 3,the semi-local convergence of the two-step combined method is pre-sented for solving the nonlinear operator equations H(x)= F(x)+ G(x)= 0 where we established semi-local convergence result and proved the uniqueness of solutions of the two-step combined method.In addition,a mumerical example is provided to illustrate our results.