Abstract. B-spline functions play important roles in both mathematics and en-gineering. In this paper, we develop a numerical method for solving the boundary value problem of linear ODE with second-order by using B-spline. First, the cubic B-spline basis functions are introduced, and then we use the linear combination of cubic B-spline basis to approximate the solution. Finally, we obtain the numerical solution by solving tri-diagonal equations. The results are compared with finite difference method and linear shooting method through an example which shows that the B-spline method is feasible and efficient. Keywords: B-spline function; Boundary-value problem; Linear shooting method; Finite difference method. 1 Introduction Ordinary Differential Equations (ODE) has a long history and widely applied in many fields. The numerical solution of ODE has made great development in the 20th century. There have been emerged many new ideas as well as many complex methods for solving ODE, so that the numerical methods for solving ODE has been deepened. Systems of ordinary differential equation have been applied to many problems in physics, engineering, biology and so on. The theory of spline functions is a very active field of approximation theory and boundary value problems (BVPs) when numerical aspects are considered. In this paper, we discuss a direct method based on B-spline for two-point boundary value problems of second-order ordinary differential equation. There are many publications dealing with this problem with some methods. For in-stance, B-spline applied to dealing with the non-linear problems [1]. A finite differ-ence method has been proposed [2]. In a series of paper by Caglar [3, 4, 5, 6] BVPs of third, fifth were solved using fourth and sixth-degree splines. B-spline method can solve linear system of second-order boundary value and singular boundary value problems etc. In the present paper, a cubic B-spline is used to solve two-point boundary value problems as the following linear systems which are assumed to have a unique solution in the interval [0, 1].
['Jincai Chang', 'Qianli Yang', 'Chunfeng Liu']
B-Spline Method for Solving Boundary Value Problems of Linear Ordinary Differential Equations