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Lloyd N. Trefethen. Spectral methods in MATLAB, volume 10. Society for Industrial and Applied Mathematics, 2000.

has been cited by the following article:

Article

Spectral Rectangular Collocation Formula: An Approach for Solving Oscillatory Initial Value Problems and/or Boundary Value Problems in Ordinary Differential Equations

1African Institute for Mathematical Sciences, Rwanda

2Department of Mathematical Sciences, Adekunle Ajasin University Akungba-Akoko, Nigeria

3EigenPoly Research Center Leuven, Belgium


Turkish Journal of Analysis and Number Theory. 2019, Vol. 7 No. 1, 11-17
DOI: 10.12691/tjant-7-1-3
Copyright © 2019 Science and Education Publishing

Cite this paper:
Oluwasegun M. Ibrahim, Piers W. Lawrence. Spectral Rectangular Collocation Formula: An Approach for Solving Oscillatory Initial Value Problems and/or Boundary Value Problems in Ordinary Differential Equations. Turkish Journal of Analysis and Number Theory. 2019; 7(1):11-17. doi: 10.12691/tjant-7-1-3.

Correspondence to: Piers  W. Lawrence, EigenPoly Research Center Leuven, Belgium. Email: oluwasegun.micheal@aims.ac.rw; piers.lawrence@eigenpoly.com

Abstract

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.

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