B-Spline Method for Solving Boundary Value Problems of Linear Ordinary Differential Equations
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- Chang J., Yang Q., Liu C. (2010) B-Spline Method for Solving Boundary Value Problems of Linear Ordinary Differential Equations. In: Zhu R., Zhang Y., Liu B., Liu C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 106. Springer, Berlin, Heidelberg
B-spline functions play important roles in both mathematics and engineering. 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.
KeywordsB-spline function Boundary-value problem Linear shooting method Finite difference method
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