Approximate Solutions of Singular Two-Point BVPs Using Legendre Operational Matrix of Differentiation

Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The accuracy of the technique is demonstrated through several linear and nonlinear test examples.

[1]  Saeed Kazem,et al.  Fractional-order Legendre functions for solving fractional-order differential equations , 2013 .

[2]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[3]  A. Kanth,et al.  Solution of singular two-point boundary value problems using differential transformation method , 2008 .

[4]  Ravi P. Agarwal,et al.  A collocation method for solving a class of singular nonlinear two-point boundary value problems , 1997 .

[5]  C. P. Katti,et al.  A Finite-difference Method for a Class of Singular Two-point Boundary-value Problems , 1984 .

[6]  Junfeng Lu,et al.  Variational iteration method for solving two-point boundary value problems , 2007 .

[7]  A. Bataineh,et al.  Approximate solutions of singular two-point BVPs by modified homotopy analysis method , 2008 .

[8]  Goutam Dutta,et al.  Solution of Lane-Emden type equations using Legendre operational matrix of differentiation , 2012, Appl. Math. Comput..

[9]  Issam Taher Mohammad Abu-Zaid.  A finite difference approximation for a class of singular boundary value problems , 1992 .

[10]  Manoj Kumar,et al.  A difference scheme based on non-uniform mesh for singular two-point boundary value problems , 2003, Appl. Math. Comput..

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

[12]  Fazhan Geng,et al.  Solving singular two-point boundary value problem in reproducing kernel space , 2007 .

[13]  Mehdi Dehghan,et al.  A new operational matrix for solving fractional-order differential equations , 2010, Comput. Math. Appl..