Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm

In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.)These problems arise when reducing partial differential equation to ordinary differential equation by physical symmetry. Some illustrative examples are given to demonstrate the efficiency and high accuracy of the proposed method and compare it to the numerical results made with other methods.