A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials

The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polyno...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry (Basel) 2023-03, Vol.15 (3), p.594
Main Authors: Abdelghany, Esraa Magdy, Abd-Elhameed, Waleed Mohamed, Moatimid, Galal Mahrous, Youssri, Youssri Hassan, Atta, Ahmed Gamal
Format: Article
Language:English
Subjects:
Basis functions
Calculus
Chebyshev approximation
Chebyshev polynomials of the sixth-kind
Error analysis
Fourier transforms
Linear algebra
Mathematical analysis
Methods
Partial differential equations
Polynomials
tau method
Temperature
Thermodynamics
time fractional heat equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polynomials of the sixth-kind (CPs6), and the second set is a set of modified shifted CPs6. The approximation of the solution is written as a product of the two chosen basis function sets. For this method, the key concept is to transform the problem governed by the underlying conditions into a set of linear algebraic equations that can be solved by means of an appropriate numerical scheme. The error analysis of the proposed extension is also thoroughly investigated. Finally, a number of examples are shown to illustrate the reliability and accuracy of the suggested tau method.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15030594