A modification of pseudo-spectral method for solving a linear ODEs with singularity

In this paper, first we introduce, briefly, pseudo-spectral method for numerical solution of ODE's and focus on those problems in which some of coefficient functions or solution function are singular. Then, by expressing weak and strong aspects of spectral methods to solve these kind of problems, a modified pseudo-spectral method which is more efficient than other spectral methods is suggested. We compare the methods with some numerical examples.