APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD

Oyedepo, Taiye; BELLO, Akanbi Kareem; Raji, Tayo Musiliu; AYINDE, Abdullahi Muhammed   AYINDE

doi:10.21608/ejmaa.2025.322389.1269

APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD

Document Type : Regular research papers

Authors

¹ Department of Applied Sciences, Federal University of Allied Health Sciences, Enugu, Nigeria.

² Department of Mathematics, University of Ilorin, Ilorin, Nigeria

³ Department of Mathematics. Federal University of Agriculture, Abeokuta.

⁴ Department of Mathematics, University of Abuja, Abuja, Nigeria

10.21608/ejmaa.2025.322389.1269

Abstract

This study explores the approximation of second-order mixed Volterra-Fredholm integro-differential equations using the Galerkin method, coupled with power series as basis functions. Integro-differential equations are pivotal in modeling various phenomena in physics and engineering, where the system's current state depends on its history. The Galerkin method is employed to derive approximate solutions by projecting the problem onto a finite-dimensional subspace spanned by chosen basis functions. This approach simplifies the solution process by reducing the integro-differential equation to a system of algebraic equations. Through numerical examples, including equations with known exact solutions, the method's effectiveness is demonstrated. The results show that the Galerkin method provides highly accurate approximations, with solutions matching the exact results for all tested cases. This validates the method's capability to handle complex integro-differential equations efficiently. The study underscores the Galerkin method’s robustness and versatility in solving integro-differential problems, highlighting its potential for broader applications in scientific and engineering disciplines.

Keywords

Main Subjects