The Research Of Fixed Point Algorithm For Solving A Class Of Nonlinear Problem

Nonlinear differential equations is one of extremely prominent branches of the modern mathematics.It is an efficient tool for solving all kinds of practical problems.It plays an important role not only in practical application,but also in theoretical research.Nonlinear differential equations are widely used to apply to some areas research such as,mechanics,geometry,physics,electronic technique,automatic control,life sciences and economy.At present,nonlinear differential equation obtained rapid application in many ways.The new problems are presented for the further development of nonlinear differential equation,it forces humans can research differential equation in depth,in order to meet the meets of the rapid development of science and technology.So to solve the numerical solution of nonlinear differential equations is becoming more and more important.Reproducing kernel space is a special Hilbert space.So,the calculation of inner product has an advantage for solving boundary value problems in reproducing kernel space.By using the fixed point iteration format,it is not only easy to calculate but also good convergence.Two kinds of methods to solving the equation,it has extremely important theory significance.This paper focuses on the study of reproducing kernel method and fixed point algorithm combining these two methods,extremely to solve third-order and fourthorder nonlinear boundary value problem.According to model features,the corresponding inner product is established by the corresponding kernel space.And then it finds the approximate solution of such equations in RKM and the fixed point methods.Finally,the effectiveness of the algorithm is verified by some numerical example.