| With the development of science and technology,more and more complex numerical calculation problems have been raised.In engineering calculation and scientific research,the practical problems can be transformed into the problem of finding the root of a nonlinear equation.Such as the calculation of electric circuits and power systems non-linear mechanics and so on.However some nonlinear equations are nondifferentiable.In this thesis,we mainly study the problem of finding roots of nondifferentiable nonlinear operator equations.The main contents of this thesis are as follows:In Chapter 1,the development of iterative methods for solving nonlinear operator equations,especially nondifferentiable operator equations,are introduced,the advantages and disadvantages of these methods compared.In Chapter 2,a family of iterative methods for solving nondifferentiable operator equations are given,the family provides a well-known method as a special case.Under some weak Lipschitz condition,the semi-local convergence theorem of this family of iter-ative methods is established,and the validity of the methods is illustrated by numerical examples.In Chapter 3,the convergence problem of a two-step iterative method is studied.On the assumption that the nonlinear nondifferentiable operator satisfies the given weak Lipschitz condition,the semi-local convergence theorem of the two-step iterative method is established.Finally,an example is given to illustrate the effectiveness of the method. |
