APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD
Oyedepo, T., BELLO, A., Raji, T., AYINDE, A. (2025). APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD. EKB Journal Management System, 13(2), 1-10. doi: 10.21608/ejmaa.2025.322389.1269
Taiye Oyedepo; Akanbi Kareem BELLO; Tayo Musiliu Raji; Abdullahi Muhammed AYINDE AYINDE. "APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD". EKB Journal Management System, 13, 2, 2025, 1-10. doi: 10.21608/ejmaa.2025.322389.1269
Oyedepo, T., BELLO, A., Raji, T., AYINDE, A. (2025). 'APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD', EKB Journal Management System, 13(2), pp. 1-10. doi: 10.21608/ejmaa.2025.322389.1269
Oyedepo, T., BELLO, A., Raji, T., AYINDE, A. APPROXIMATION OF SECOND ORDER MIXED VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY GALERKIN METHOD. EKB Journal Management System, 2025; 13(2): 1-10. doi: 10.21608/ejmaa.2025.322389.1269

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

Electronic Journal of Mathematical Analysis and Applications
Volume 13, Issue 2, 2025, Page 1-10  XML PDF (407.77 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2025.322389.1269
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Authors
Taiye Oyedepo email orcid 1; Akanbi Kareem BELLOorcid 2; Tayo Musiliu Rajiorcid 3; Abdullahi Muhammed AYINDE AYINDEorcid 4
1Department of Applied Sciences, Federal University of Allied Health Sciences, Enugu, Nigeria.
2Department of Mathematics, University of Ilorin, Ilorin, Nigeria
3Department of Mathematics. Federal University of Agriculture, Abeokuta.
4Department of Mathematics, University of Abuja, Abuja, Nigeria
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
Power series; Galerkin method; Integro-differential equations; Residual equation
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