Research On Numerical Solution Of Second Order Singular Boundary-value Problems Based On Spline Function

Most of differential equations arise from the practical engineering problems whose analytical solutions are difficult to obtain.therefor,the research of numerical of differential equations is very important and necessary.Splines are applied widely in function approximation,computational geometry, CAGD,finite element,wavelet, numerical solutions of differential equations and so on. On the basis of predecessors .In this paper,we study the numerical solution methods based on cubic splines for solving a class of singular boundary value problems.The two methods are given for solving the numerical solution and some numerical examples have been solved to demonstrate the efficiency and feasibility of the method.Chapter 1:Introduce the importance of numerical solution of differential equation and investigative background of singular differential equations and some basic concepts and knowledge.Chapter 2:Discusses the numerical solution methods of singular boundary value problems.sum up and compare the forepassed,recent existent numerical method, mainly invloves three aspects:No1, B-spline solution of singular boundary value problems and some numerical examples.No2:Higher order finite difference method and some numerical examples. No3:Cubic splines solutions for singular boundary value problems.Chapter 3:Discusses the application of cubic splines to solve the singular boundary value problems.Based on the results,the article do the work as follow:we ues three points difference of second derivative and five points difference of first derivative to modify the cubic spline, some numerical examples have been solved to demonstrate the efficiency and feasibility of the method.Chapter 4:Introduce the cubic spline methods to apply in other types of partial differential equations.Chapter 5 Summarizes the whole dissertation and gives some expectation for future Research.