Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel

This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up a new Hilbert space that satisfies the initial and boundary conditions. The new spectra...

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Bibliographic Details
Published in:Computational & applied mathematics 2022-12, Vol.41 (8), Article 381
Main Authors: Atta, A. G., Youssri, Y. H.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Basis functions
Boundary conditions
Chebyshev approximation
Collocation methods
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Error analysis
Hilbert space
Kernels
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Polynomials
Spectral methods
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Summary:This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up a new Hilbert space that satisfies the initial and boundary conditions. The new spectral collocation approach is applied to obtain precise numerical approximation using new basis functions based on shifted first-kind Chebyshev polynomials (SCP1K). Furthermore, we support our study by a careful error analysis of the suggested shifted first-kind Chebyshev expansion. The results show that the new approach is very accurate and effective.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-02096-7