A quartic B-spline for second-order singular boundary value problems

Second-order singular boundary value problems are treated using quartic (fourth-degree) B-spline approximations. The values of the coefficients, C"i, are chosen via optimization. Error analysis is discussed. The efficiency of the method is illustrated with several problems from the literature.

[1]  Lawrence F. Shampine,et al.  Numerical Methods for Singular Boundary Value Problems , 1975 .

[2]  Zhongdi Cen,et al.  Numerical study for a class of singular two-point boundary value problems using Green's functions , 2006, Appl. Math. Comput..

[3]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[4]  A. S. V. Ravi Kanth,et al.  Cubic spline polynomial for non-linear singular two-point boundary value problems , 2007, Appl. Math. Comput..

[5]  W. D. Hoskins,et al.  Cubic spline solutions to two-point boundary value problems , 1969, Comput. J..

[6]  Ahmad Abdul Majid,et al.  Numerical method using cubic B-spline for the heat and wave equation , 2011, Comput. Math. Appl..

[7]  M. K. Kadalbajoo,et al.  Numerical solution of singular boundary value problems via Chebyshev polynomial and B-spline , 2005, Appl. Math. Comput..

[8]  A. S. V. Ravi Kanth,et al.  A numerical method for singular two point boundary value problems via Chebyshev economizition , 2003, Appl. Math. Comput..

[9]  A. S. V. Ravi Kanth,et al.  Higher order finite difference method for a class of singular boundary value problems , 2004, Appl. Math. Comput..

[10]  M. K. Kadalbajoo,et al.  B-spline method for a class of singular two-point boundary value problems using optimal grid , 2007, Appl. Math. Comput..

[11]  Manoj Kumar,et al.  Methods for solving singular boundary value problems using splines: a review , 2010 .

[12]  Hikmet Caglar,et al.  B-spline solution of singular boundary value problems , 2006, Appl. Math. Comput..

[13]  W. G. Bickley,et al.  Piecewise Cubic Interpolation and Two-Point Boundary Problems , 1968, Comput. J..

[14]  P. M. Prenter Splines and variational methods , 1975 .

[15]  D. J. Fyfe,et al.  The use of cubic splines in the solution of two-point boundary value problems , 1969, Comput. J..

[16]  Hikmet Caglar,et al.  B-spline solution of non-linear singular boundary value problems arising in physiology , 2009 .

[17]  A. S. V. Ravi Kanth,et al.  Cubic spline for a class of singular two-point boundary value problems , 2005, Appl. Math. Comput..

[18]  H. Keller Numerical Methods for Two-Point Boundary-Value Problems , 1993 .

[19]  Lawrence F. Shampine,et al.  Singular boundary value problems for ODEs , 2003, Appl. Math. Comput..

[20]  Manoj Kumar A difference method for singular two-point boundary value problems , 2003, Appl. Math. Comput..

[21]  Bo Han,et al.  A new method for solving a class of singular two-point boundary value problems , 2008, Appl. Math. Comput..