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Accurate spectral algorithm for two‐dimensional variable‐order fractional percolation equations
Author(s) -
Abdelkawy Mohamed A.,
Mahmoud Emad E.,
Abualnaja Kholod M.,
AbdelAty AbdelHaleem,
Kumar Sunil
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7195
Subject(s) - mathematics , legendre polynomials , collocation (remote sensing) , gauss , percolation (cognitive psychology) , variable (mathematics) , order (exchange) , spectral method , chebyshev filter , fractional calculus , chebyshev polynomials , collocation method , algorithm , mathematical analysis , physics , computer science , ordinary differential equation , finance , quantum mechanics , machine learning , neuroscience , economics , biology , differential equation
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.