Novel and accurate Gegenbauer spectral tau algorithms for distributed order nonlinear time-fractional telegraph models in multi-dimensions

This paper sheds light on the numerical solutions of the multi-dimensional distributed-order (DO) nonlinear time-fractional telegraph equations (TFTEs) models. We present novel and accurate shifted Gegenbauer spectral tau schemes for solving the aforementioned models. In the proposed schemes, the kn...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 118; p. 107062
Main Authors: Ahmed, Hoda F., Hashem, W.A.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2023
Subjects:
Distributed order
Gegenbauer polynomials
Nonlinear time-fractional telegraph models
Operational matrices
Spectral tau method
Spectral tau method
Gegenbauer polynomials
Distributed order
Operational matrices
Nonlinear time-fractional telegraph models
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:This paper sheds light on the numerical solutions of the multi-dimensional distributed-order (DO) nonlinear time-fractional telegraph equations (TFTEs) models. We present novel and accurate shifted Gegenbauer spectral tau schemes for solving the aforementioned models. In the proposed schemes, the known and unknown functions are approximated in terms of the shifted Gegenbauer polynomials (SGPs) by using the Kronecker product structure in time and space. The matrix representation of the DO fractional derivative of SGPs in the Caputo sense has been derived. Also, novel operational matrices of the multiplication of shifted Gegenbauer functions in multi-dimension have been constructed to remove the obstacle that facing the use of the tau method in the presence of nonlinear term or variable coefficients or both of them. The proposed method takes full advantage of the nonlocal nature of DO fractional differential operators. The presented method is applied on six miscellaneous test examples to illustrate its robustness and effectiveness for smooth and non smooth solutions. •Multi-dimensional distributed-order nonlinear time-fractional telegraph models.•The operational matrices of the multiplication of shifted Gegenbauer vectors.•The shifted Gegenbauer operational matrix of the distributed fractional derivative.•Novel and accurate spectral tau method for the proposed multi-dimensional models.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2022.107062