Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation

In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linea...

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Bibliographic Details
Published in:Nonlinear engineering 2023-08, Vol.12 (1), p.5652-61
Main Authors: Moustafa, Mohamed, Youssri, Youssri Hassan, Atta, Ahmed Gamal
Format: Article
Language:English
Subjects:
35R11
42C05
65G99
65M70
Algorithms
Chebyshev approximation
Chebyshev polynomials
error analysis
Galerkin method
Gaussian elimination
Linear algebra
Petrov–Galerkin method
Polynomials
Thermal expansion
time-fractional fourth-order partial differential equations
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Summary:In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linear algebraic equations with unknown expansion coefficients. Using the efficient Gaussian elimination procedure, we solve the obtained system of equations with matrices of a particular pattern. The and norms estimate the error bound. Three numerical examples were exhibited to verify the theoretical analysis and efficiency of the newly developed algorithm.
ISSN:2192-8029
2192-8010
2192-8029
DOI:10.1515/nleng-2022-0308