A fourth-order spline finite difference method for singular two-point boundary value problems

In this paper we discuss the construction of a spline function for a class of singular two-point boundary value problems Five point finite difference method using the above splines, obtained is shown to be order h 4 convergent for all α ∈ (0, 1). The method is illustrated computationally.

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

[2]  Manoj Kumar,et al.  A three-point finite difference method for a class of singular two-point boundary value problems , 2002 .

[3]  A New Fourth Order Cubic Spline Method for Non-Linear Two-Point Boundary Value Problems , 1987 .

[4]  Manabu Sakai,et al.  Piecewise Cubic Interpolation and Two-Point Boundary Value Problems , 1971 .

[5]  S. R. K. Iyengar,et al.  Spline finite difference methods for singular two point boundary value problems , 1986 .

[6]  M. M. Chawla,et al.  Finite difference methods and their convergence for a class of singular two point boundary value problems , 1982 .

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

[8]  A fourth-order finite difference method based on uniform mesh for singular two-point boundary-value problems , 1987 .

[9]  M. Chawla,et al.  A new fourth-order cubic spline method for second-order nonlinear two-point boundary-value problems , 1988 .

[10]  Pierre Jamet On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems , 1970 .

[11]  Philippe G. Ciarlet,et al.  Numerical methods of high-order accuracy for singular nonlinear boundary value problems , 1970 .

[12]  Tariq Aziz,et al.  A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems , 2001 .