Numerical solution of singular boundary value problems with logarithmic singularities by Padé approximation and collocation methods

In this paper, we present a method using quintic B-spline and Padé approximation for numerically solving singular boundary value problems, for certain ordinary differential equation having singular coefficient, we use the modified quintic B-spline to approximate the first coefficients in the Taylor expansion, on which all the other coefficients depend. Moreover, we introduce the superposed Padé approximation. The resulting perturbed initial value problem is then efficiently treated.