Work

Derivation and Implementation of the CollocationMethods for Solving Single and Multi TimeFractional Order Differential Equations

Year: 2025

Type: article

Abstract: Standard collocation (SCM) and perturbed collocation (PCM) are utilized as effective numerical techniques for solving fractional-order differential equations (FODEs) which focus on constructing orthogonal polynomials to serve as basis functions for approximating the solutions to these equations.The approach began by assuming an approximate solution, expressed in the constructed orthogonal polynomials.These assumed solutions were then substituted into the original FODEs.Following this, the problem was converted into a system of algebraic linear equations by collocating the equations at evenly spaced interior points.Numerical examples and the results indicated that the SCM and PCM are easy, efficient, and in good agreement compared with some existing methods and the results presented in the tables and graphs unequivocally demonstrate the efficacy of the proposed methods in solving fractional-order differential equations, yielding solutions of remarkable accuracy.However, the SCM and PCM exhibit comparable accuracy, making it difficult to identify a single superior approach, we conclude that both the proposed methods are effective and viable options for solving fractional order differential equations.

Source: International Journal of Mathematical Sciences and Computing

DOI: 10.5815/ijmsc.2025.01.03

Authors: Falade Kazeem Iyanda, Muhammad Yusuf Muhammad, Taiwo Omotayo Adebayo, Adeyemo Kolawole Adefemi

Institutions: University of Ilorin, Nigeria Police Academy

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Texas Emerging Technology Fund

OpenAlex ID: W4409109031