Fast-Stable Collocation Method For Solving High Order Nonlinear Two-Point Boundary Value Problem

High order nonlinear two-point boundary value problem is widely used in engineering,but the high order nonlinear two-point boundary value problem is generally difficult to obtain exact solutions.So it is very important to find a more precise,simpler,faster and more stable method for obtaining numerical solutions of high order nonlinear two-point boundary value problem.The collocation method is a method for solving differential equations and it is a property way to solve high order nonlinear two-point boundary value problem.In this paper,the Newton's iterative method is used to linearize the nonlinear equations,and then we can obtain the linear two-point boundary value problem.According to the specific form of the linear two-point boundary value problem,the reproducing kernel space is determined.We define the mapping on the dense subspace of the squared integrable space,construct a set of substrates on the dense subspace of the reproducing kernel space,complete the proof of density,and use the collocation method combined with the least squares method to give the ?-approximate solution of the linear operator equation.At the same time,the proof of the stability of the method is given.Finally,the effectiveness of the proposed algorithm is verified by comparison with other numerical methods.