A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time optimization problem to a discrete time optimization problem. By solving the discrete time optimization problem, we find discrete approximations for the solutions of the main singular boundary value problem. Also, by Lagrange interpolation we obtain a continuous approximation for the solution. The efficiency and the reliability of the proposed approach are tested by solving three practical singular boundary value problems.

Keywords:

Singular boundary value problem , Chebyshev polynomial , Continuous time optimization problem , Discrete optimization problem