Approximate Solutions of Fourth Order Volterra Integro-Differential Equations Based on Chebyshev Polynomials
Otaide Ikechukwu Jackson *
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
Agwemuria Oghenefejiro Richard
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
Damisa John Sijuola
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
Utoyo Ovokaefe Trust
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
Egborge Oghenerukevwe Usu
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
Salami Matthew Ophokpokpo
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this work, shifted Chebyshev polynomials of the second kind and the variational iteration approach (VIA) are used to numerically solve fourth order Volterra integro-differential equations. The suggested method is then applied, and the trial functions for the approximation are the shifted Chebyshev polynomials of the second kind produced for the specified Volterra integro-differential equation. The importance of the proposed approach therefore most likely extends beyond a specific equation or application since it advances the broader domain of mathematical modeling and numerical analysis. The goal of research methodologies that combine a basis function and variational iteration approach (VIA) is to offer universal procedures that may be used to solve a variety of problems. To further demonstrate the reliability and applicability of the suggested method, four numerical examples were presented. The numerical outcome shows that the suggested technique outperforms method in literature. The Maple 18 software was used to perform the mathematical calculations.
Keywords: Variational iteration approach (VIA), Volterra integro-differential equation, second kind Chebyshev polynomials, approximate solutions