A hybrid spectral approach based on 2D cardinal and classical second kind Chebyshev polynomials for time fractional 3D Sobolev equation

In this work, the Caputo fractional derivative defines the time fractional 3D Sobolev equation. The 2D shifted second kind Chebyshev cardinal polynomials (SSKCCPs) and 2D shifted second kind Chebyshev polynomials (SSKCPs) (as two well‐known classes of basis functions) are utilized to establish a hyb...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-12, Vol.46 (18), p.18768-18788
Main Authors: Hosseininia, M., Heydari, M. H., Razzaghi, M.
Format: Article
Language:English
Subjects:
Algorithms
Basis functions
Chebyshev approximation
Collocation methods
Mathematical analysis
Polynomials
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Summary:In this work, the Caputo fractional derivative defines the time fractional 3D Sobolev equation. The 2D shifted second kind Chebyshev cardinal polynomials (SSKCCPs) and 2D shifted second kind Chebyshev polynomials (SSKCPs) (as two well‐known classes of basis functions) are utilized to establish a hybrid technique for this new problem. First, the problem solution is approximated simultaneously using the 2D SSKCCPs (relative to ) and 2D SSKCCPs (relative to ). Next, the classical and fractional operational matrices of these polynomials are achieved and applied to make the hybrid algorithm. With a combination of derived operational matrices and the collocation approach, solving the expressed fractional 3D problem turns into solving an equivalent system of algebraic equations. The proposed algorithm's accuracy is checked using four numerical examples.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9592