A modified spectral method for numerical solution of ordinary differential equations with non-analytic solution

Abstract

In this article, there is an attempt to introduce, generally, spectral methods for numerical solution of ordinary differential equations, also, to focus on those problems in which some coefficient functions or solution function is not analytic. Then, by expressing weak and strong aspects of spectral methods to solve this kind of problems, a modified spectral method which is more efficient than other spectral methods is suggested. Furthermore, with providing some examples, the aforementioned cases are dealt with numerically.