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

Oluwasegun M. Ibrahim^{1, 2,} and Piers W. Lawrence^3,

¹African Institute for Mathematical Sciences, Rwanda

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

³EigenPoly Research Center Leuven, Belgium

Cite this paper:
Oluwasegun M. Ibrahim and 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

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.

Keywords:
spectral rectangular collocation polynomial interpolation oscillatory solutions initial value problems boundary value problems ordinary differential equations.

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