Numerical Methods Based on the Hybrid Shifted Orthonormal Polynomials and Block‐Pulse Functions for Solving a System of Fractional Differential Equations

This paper develops two numerical methods for solving a system of fractional differential equations based on hybrid shifted orthonormal Bernstein polynomials with generalized block‐pulse functions (HSOBBPFs) and hybrid shifted orthonormal Legendre polynomials with generalized block‐pulse functions (...

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Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2024; no. 1
Main Authors Rageh, Abdulqawi A. M., Hadhoud, Adel R.
Format Journal Article
LanguageEnglish
Published Hoboken Hindawi Limited 01.01.2024
Wiley
Subjects
Accuracy
Differential equations
Error analysis
Fractional calculus
Hybrid systems
Integral equations
Mathematical analysis
Methods
Numerical analysis
Numerical methods
Partial differential equations
Polynomials
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Summary:This paper develops two numerical methods for solving a system of fractional differential equations based on hybrid shifted orthonormal Bernstein polynomials with generalized block‐pulse functions (HSOBBPFs) and hybrid shifted orthonormal Legendre polynomials with generalized block‐pulse functions (HSOLBPFs). Using these hybrid bases and the operational matrices method, the system of fractional differential equations is reduced to a system of algebraic equations. Error analysis is performed and some simulation examples are provided to demonstrate the efficacy of the proposed techniques. The numerical results of the proposed methods are compared to those of the existing numerical methods. These approaches are distinguished by their ability to work on the wide interval [0, a ], as well as their high accuracy and rapid convergence, demonstrating the utility of the proposed approaches over other numerical methods.
ISSN:1076-2787
1099-0526
DOI:10.1155/2024/6302827