Jacobi spectral method for variable-order fractional Benney–Lin equation arising in falling film problems

In this paper, a variable-order fractional version of the Benney–Lin equation is defined using the variable-order fractional derivative in the Caputo type. A collocation method based on the shifted Jacobi polynomials is applied to deal with this problem. Some matrix relationships related to these po...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2022-03, Vol.402, p.113813, Article 113813
Main Authors: Heydari, M.H., Razzaghi, M.
Format: Article
Language:English
Subjects:
Benney–Lin equation
Jacobi polynomials
Jacobi–Gauss–Lobatto quadrature technique
Variable-order fractional derivative matrix
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Summary:In this paper, a variable-order fractional version of the Benney–Lin equation is defined using the variable-order fractional derivative in the Caputo type. A collocation method based on the shifted Jacobi polynomials is applied to deal with this problem. Some matrix relationships related to these polynomials are extracted and used in constructing the established method. The obtained relations cause the method calculations to be significantly reduced, which reduce the method execution time. The established technique converts solving the problem under study into solving an algebraic system of equations. The high accuracy and low computations of the presented scheme are investigated by solving some numerical examples.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113813