Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions

The distributed-order fractional telegraph models are commonly used to describe the phenomenas of diffusion and wave-like anomalous, which can model processes without a power-law scale across the entire temporal domain. To increase the range of implementation of distributed-order fractional telegrap...

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Bibliographic Details
Published in:Numerical algorithms Vol. 93; no. 3; pp. 1013 - 1043
Main Authors: Ahmed, Hoda F., Hashem, W. A.
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2023
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
Boundary conditions
Computer Science
Error analysis
Matrix representation
Methods
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Robustness (mathematics)
Theory of Computation
Spectral tau method
Gegenbauer polynomials
Error analysis
Fractional telegraph models
Operational matrices
Distributed-order
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The distributed-order fractional telegraph models are commonly used to describe the phenomenas of diffusion and wave-like anomalous, which can model processes without a power-law scale across the entire temporal domain. To increase the range of implementation of distributed-order fractional telegraph models, there is a need to present effective and accurate numerical algorithms to solve these models, as these models are hard to solve analytically. In this work, a novel matrix representation of the distributed-order fractional derivative based on shifted Gegenbauer (SG) polynomials has been derived. Also, two efficient algorithms based on the aforementioned operatonal matrix and the spectral tau method have been constructed for solving the one- and two-dimensional (1D and 2D) distributed-order time-fractional telegraph models with spatial variable coefficients. Also, a new operational matrix of the multiplication of space vectors has been built to have the ability in applying the tau method in the 2D case. The convergence and error bound analysis of the presented techniques are investigated. Moreover, the presented algorithms are applied on four miscellaneous test examples to illustrate the robustness and effectiveness of these algorithms.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01452-2