Several Higher Order Methods For Solving Nonlinear Equations

With the progress of modern science and technology,there are many nonlinear problems in many fields of scientific innovation,such as petroleum geological survey,astronomical and meteorological data analysis,missile launch orbit planning,train ship route and aerospace field,etc.However,solving the nonlinear equation(group)is not easy to get the exact solution in the actual operation,so it is changed to the numerical solution.Among them,iterative method is the most important method to solve the numerical solution problem of nonlinear equation.In this paper,several higher order iterative methods for solving nonlinear equations are constructed by using undetermined coefficient method and weight function method.The goal of constructing the new iterative method is to use less computational cost and improve the computational efficiency and convergence order as much as possible.First of all,the research status of nonlinear equation(group)iterative method and the related basic concepts are briefly introduced.Then,based on the Steffensen iterative method,a new optimal fourth-order derivativeless two-step iterative method for solving nonlinear equations is constructed.After that,based on the Ostrowski iterative method,a Newton-type iterative method for solving the eighth order convergence of nonlinear equations is proposed by using the weight function method,and combining the experimental data.Finally,an optimal fourth-order Steffensen iterative method for solving nonlinear systems is constructed,and the iterative method is used to solve the initial value problem of nonlinear ordinary differential systems.The experimental data show that the iterative method is efficient.