Least Squares Approximation Method for Estimation of Volterra Fractional Integro-differential equation using Hermite Polynomial as the basis functions
Year: 2024
Type: article
Abstract: This research work utilizes the least squares approximation method to estimate approximate solutions for fractional-order integro-differential equations, with Hermite polynomials as basis functions. The process begins by assuming an approximate solution of degree N, which is then substituted into the fractional-order integro-differential equation under investigation. After evaluating the integral, the equation is rearranged to isolate one side, allowing the application of the least squares method. Three examples were solved using this approach. In Example 1, the numerical results for α=0.9 and α=0.8 were compared to the exact solution for α=1. In Examples 2 and 3, the results for α=1.9 and α=1.8 were compared to the exact solution for α=2. These comparisons showed favorable alignment with the exact solutions. The numerical results and graphical illustrations demonstrate the validity, competence, and accuracy of the proposed method.
DOI: 10.14419/xm3rsy98
Authors: Ayodeji Akinsanya, Gabriel Agholor
Institution: University of Ilorin
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403703977