Legendre Collocatıon for Sıx Order Boundary Value Problems

Authors

Taiye Oyedepo, Department of Applied Sciences, Federal College of Dental Technology and Therapy, Enugu, NigeriaFollow
Abayomi Ayotunde Ayoade, Department of Mathematics, University of Lagos, Lagos, Nigeria
Ganiyu Ajileye, Department of Mathematics and Statistics, Federal University Wukari Taraba, Nigeria
Rajiniganth Pandurangan, Department of Mathematics, Dhanalakshmi Srinivasan University, Samayapuram-621112, Tiruchirapalli, Tamil Nadu, India

Document Type

Original Study

Abstract

The study aims to employ Legendre polynomials as basis functions for numerically solving six-order Boundary Value Problems (BVPs). Through the utilization of collocation points, the method transforms the differential problem into a system of algebraic equations, subsequently solved through matrix inversion. The research delves into the convergence and error analysis of this technique and validates its effectiveness through discussion of three test problems. The proposed approach provides highly accurate results, closely approximating the exact solution. The study illustrates its precision and efficacy through tables and figures, showcasing its superiority over other methods discussed in the literature.

Keywords

Legendre polynomials, boundary value problems, collocation approach approximate solution

Recommended Citation

Oyedepo, Taiye; Ayoade, Abayomi Ayotunde; Ajileye, Ganiyu; and Pandurangan, Rajiniganth (2024) "Legendre Collocatıon for Sıx Order Boundary Value Problems," Al-Qadisiyah Journal of Pure Science: Vol. 29 : No. 1 , Article 16.
Available at: https://doi.org/10.29350/2411-3514.1249

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.