B-Spline Method for Solving Boundary Value Problems of Linear Ordinary Differential Equations

  • Jincai Chang
  • Qianli Yang
  • Chunfeng Liu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 106)


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.


B-spline function Boundary-value problem Linear shooting method Finite difference method 


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  1. 1.
    Caglar, H., Caglar, N., Ozer, M.: B-spline solution of non-linear singular boundary value problems arising in physiology. Chaos, Soli. and Frac. 39, 1232–1237 (2009)CrossRefMATHGoogle Scholar
  2. 2.
    Chawla, M.M., Katti, C.P.: A finite difference method for a class of singular two point boundary value problems. IMA. J. Number. Anal. 4, 457–466 (1984)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Caglar, N., Caglar, H.: B-spline method for solving linear system of second-order boundary value problems. Comp. and Math. with Appl. 57, 757–762 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Caglar, N., Caglar, H.: B-spline solution of singular boundary value problems. Appl. Math. and Comp. 182, 1509–1513 (2006)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Caglar, H.N., Caglar, S.H., Twizell, E.H.: The numerical solution of third-order Boundary value problems with fourth-degree B-spline funtions. Int. J. Comput. Math. 71, 373–381 (1999)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Caglar, H.N., Caglar, S.H., Twizell, E.H.: The numerical solution of fifth-order boundary value problems with sixth-degree B-spline funtions. Appl. Math. Lett. 12, 25–30 (1999)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Wang, R.H., Li, C.J., Zhu, C.G.: Computational Geometry. Science Press, Beijing (2008)Google Scholar
  8. 8.
    Caglar, H., Caglar, N., Eifaituri, K.: B-spline interpolation compared with finite difference, finite element and finite volume methods with applied to two-point boundary value problems. Appl. Math. and Comp. 175, 72–79 (2006)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ren, Y.J.: Numerical Analysis and MATLAB Implementation. Higher Education Press, Beijing (2008)Google Scholar
  10. 10.
    Zhu, C.G., Kang, W.S.: Numerical solution of Burgers-Fisher equation by cubic B-spline quasi-interpolation. Appl. Math. and Comp. 216, 2679–2686 (2010)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jincai Chang
    • 1
  • Qianli Yang
    • 1
  • Chunfeng Liu
    • 1
  1. 1.College of ScienceHebei Polytechnic UniversityTangshanChina

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