Collocation approximation methods for solving higher-order ordinary differential equations
Author(s): Ayinde Muhammed Abdullahi, Ishaq Ajimoti Adam, Oyedepo Taiye and Alkali Mohammed Adamu
Abstract: In this work, we use the standard collocation method to estimate the solution of higher-order initial value problems (IVPs) in ordinary differential equations (ODEs) by utilizing shifted Chebyshev and shifted Legendre polynomials as basis functions. The ODEs were transformed to integral equations first, then the basis function was substituted to produce a set of linear algebraic equations that were solved using Maple 18. In terms of errors, comparisons were made with the two trial solutions indicated above. To demonstrate the method's performance for varied orders, numerical examples were provided. The shifted Chebyshev polynomial (SCP) basis, on the other hand, outperforms the shifted Legendre polynomial in terms of accuracy, as evidenced by the error tables (SLP).
Ayinde Muhammed Abdullahi, Ishaq Ajimoti Adam, Oyedepo Taiye, Alkali Mohammed Adamu. Collocation approximation methods for solving higher-order ordinary differential equations. Int J Res Civ Eng Technol 2022;3(1):26-35.