Accurate spectral algorithm for two-dimensional variable-order fractional percolation equations

Mohamed A. Abdelkawy; Emad E. Mahmoud; Kholod M. Abualnaja; Abdel Haleem Abdel-Aty; Sunil Kumar

doi:10.1002/mma.7195

Accurate spectral algorithm for two-dimensional variable-order fractional percolation equations

Mohamed A. Abdelkawy
, Emad E. Mahmoud
, Kholod M. Abualnaja
, Abdel Haleem Abdel-Aty
, Sunil Kumar

Al-Imam Muhammad Ibn Saud Islamic University
Faculty of Sciences
Taif University
Umm Al-Qura University
University of Bisha
Al-Azhar University
National Institute of Technology Jamshedpur

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A highly accurate spectral algorithm for (2 + 1) fractional percolation equations with variable order (VO-FPEs) is considered. We propose a shifted Legendre–Gauss–Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev–Gauss–Radau collocation (SC-GR-C) method to solve the two-dimensional VO-FPEs. A complete theoretical formulation is presented, and numerical results are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle VO-FPEs is revealed, even when dealing with non-smooth time solutions.

Original language	English
Pages (from-to)	6228-6238
Number of pages	11
Journal	Mathematical Methods in the Applied Sciences
Volume	44
Issue number	7
DOIs	https://doi.org/10.1002/mma.7195
State	Published - 15 May 2021
Externally published	Yes

Keywords

collocation method
fractional derivatives
shifted Chebyshev–Gauss–Radau quadrature
shifted Legendre–Gauss–Lobatto quadrature
variable-order fractional nonlinear percolation equations

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10.1002/mma.7195

Cite this

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title = "Accurate spectral algorithm for two-dimensional variable-order fractional percolation equations",

abstract = "A highly accurate spectral algorithm for (2 + 1) fractional percolation equations with variable order (VO-FPEs) is considered. We propose a shifted Legendre–Gauss–Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev–Gauss–Radau collocation (SC-GR-C) method to solve the two-dimensional VO-FPEs. A complete theoretical formulation is presented, and numerical results are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle VO-FPEs is revealed, even when dealing with non-smooth time solutions.",

keywords = "collocation method, fractional derivatives, shifted Chebyshev–Gauss–Radau quadrature, shifted Legendre–Gauss–Lobatto quadrature, variable-order fractional nonlinear percolation equations",

author = "Abdelkawy, \{Mohamed A.\} and Mahmoud, \{Emad E.\} and Abualnaja, \{Kholod M.\} and Abdel-Aty, \{Abdel Haleem\} and Sunil Kumar",

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doi = "10.1002/mma.7195",

language = "English",

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T1 - Accurate spectral algorithm for two-dimensional variable-order fractional percolation equations

AU - Abdelkawy, Mohamed A.

AU - Mahmoud, Emad E.

AU - Abualnaja, Kholod M.

AU - Abdel-Aty, Abdel Haleem

AU - Kumar, Sunil

PY - 2021/5/15

Y1 - 2021/5/15

N2 - A highly accurate spectral algorithm for (2 + 1) fractional percolation equations with variable order (VO-FPEs) is considered. We propose a shifted Legendre–Gauss–Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev–Gauss–Radau collocation (SC-GR-C) method to solve the two-dimensional VO-FPEs. A complete theoretical formulation is presented, and numerical results are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle VO-FPEs is revealed, even when dealing with non-smooth time solutions.

AB - A highly accurate spectral algorithm for (2 + 1) fractional percolation equations with variable order (VO-FPEs) is considered. We propose a shifted Legendre–Gauss–Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev–Gauss–Radau collocation (SC-GR-C) method to solve the two-dimensional VO-FPEs. A complete theoretical formulation is presented, and numerical results are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle VO-FPEs is revealed, even when dealing with non-smooth time solutions.

KW - collocation method

KW - fractional derivatives

KW - shifted Chebyshev–Gauss–Radau quadrature

KW - shifted Legendre–Gauss–Lobatto quadrature

KW - variable-order fractional nonlinear percolation equations

UR - https://www.scopus.com/pages/publications/85099845292

U2 - 10.1002/mma.7195

DO - 10.1002/mma.7195

M3 - Article

AN - SCOPUS:85099845292

SN - 0170-4214

VL - 44

SP - 6228

EP - 6238

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 7

ER -

Accurate spectral algorithm for two-dimensional variable-order fractional percolation equations

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Keywords

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