eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-02-20 7 1 11 17 10.12691/tjant-7-1-3 TJANT2019713 article Oluwasegun M. Ibrahim oluwasegun.micheal@aims.ac.rw; piers.lawrence@eigenpoly.com 1 2 Piers W. Lawrence oluwasegun.micheal@aims.ac.rw; piers.lawrence@eigenpoly.com 3 African Institute for Mathematical Sciences, Rwanda EigenPoly Research Center Leuven, Belgium The idea of rectangularization of a differentiation matrix through collocation was recently suggested to be more useful in discretization process, especially when the traditional row replacement approach fails. In this regard, we employ the state-of-the-art technique of rectangularization to discretize some oscillatory initial value problems (IVPs) and also extended the new approach to a non-linear boundary value problem (BVP). The numerical implementation was composed using some few lines of executable Python codes. Our findings are instructive and quite revealing and supported by evidence from our numerical experiments and simulations. http://pubs.sciepub.com/tjant/7/1/3/tjant-7-1-3.pdf spectral rectangular collocation polynomial interpolation oscillatory solutions initial value problems boundary value problems ordinary differential equations