VIETA-LUCAS POLYNOMIAL COMPUTATIONAL TECNIQUE FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
Oyedepo, T., Ayinde, A., Didigwu, E. (2024). VIETA-LUCAS POLYNOMIAL COMPUTATIONAL TECNIQUE FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS. EKB Journal Management System, 12(1), 1-8. doi: 10.21608/ejmaa.2023.232998.1064
Taiye Oyedepo; Abdullahi Muhammed Ayinde; Edith Ndidiamaka Didigwu. "VIETA-LUCAS POLYNOMIAL COMPUTATIONAL TECNIQUE FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS". EKB Journal Management System, 12, 1, 2024, 1-8. doi: 10.21608/ejmaa.2023.232998.1064
Oyedepo, T., Ayinde, A., Didigwu, E. (2024). 'VIETA-LUCAS POLYNOMIAL COMPUTATIONAL TECNIQUE FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS', EKB Journal Management System, 12(1), pp. 1-8. doi: 10.21608/ejmaa.2023.232998.1064
Oyedepo, T., Ayinde, A., Didigwu, E. VIETA-LUCAS POLYNOMIAL COMPUTATIONAL TECNIQUE FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS. EKB Journal Management System, 2024; 12(1): 1-8. doi: 10.21608/ejmaa.2023.232998.1064

VIETA-LUCAS POLYNOMIAL COMPUTATIONAL TECNIQUE FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Electronic Journal of Mathematical Analysis and Applications
Volume 12, Issue 1, January 2024, Page 1-8  XML PDF (431.19 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2023.232998.1064
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Authors
Taiye Oyedepo email orcid 1; Abdullahi Muhammed Ayindeorcid 2; Edith Ndidiamaka Didigwu3
1Department of Applied Sciences, Federal College of Dental Technology and Therapy, Enugu, Nigeria.
2Department of Mathematics, University of Abuja, Nigeria
3Department of Industrial Mathematics/Applied Statistics, Enugu State University of Science and Technology, Enugu, Nigeria
Abstract
In this study, we introduce a computational technique for tackling Volterra Integro-Differential Equations (VIDEs) using shifted Vieta-Lucas polynomials as the foundational basis functions. The approach involves adopting an approximative solution strategy through the utilization of Vieta-Lucas polynomials. These polynomials are then integrated into the pertinent Volterra Integro-Differential Equations (VIDEs). Subsequently, the resulting equation is subjected to collocation at evenly spaced intervals, generating a system of linear algebraic equations with unspecified Vieta-Lucas coefficients. To solve this system, we employ a matrix inversion method to deduce the unknown constants. Once these constants are determined, they are incorporated into the earlier assumed approximate solution, thus yielding the sought-after approximated solution. To validate the accuracy and efficiency of this technique, we conducted numerical experiments. The obtained results underscore the outstanding performance of our method in comparison to outcomes found in existing literature. The precision and effectiveness of the approach are further illustrated through the utilization of tables.
Keywords
Vieta-Lucas polynomials; colloation method; Volterra integro-differential equations; approximate solution; matrix inversion
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