Buchumschlag

Hexic-Chebyshev Collocation Method for Solving Distributed-Order Time-Space Fractional Diffusion Equations

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Veröffentlicht in:Axioms vol. 14, no. 7 (2025), p. 515-536
1. Verfasser: Babaei Afshin
Weitere Verfasser: Banihashemi Sedigheh, Moghaddam, Behrouz Parsa, Dabiri Arman
Veröffentlicht:
MDPI AG
Schlagworte:
Accuracy
Calculus
Mathematical analysis
Polynomials
Collocation methods
Newton-Raphson method
Chebyshev approximation
Numerical analysis
Methods
Algebra
Efficiency
Nonlinearity
Spectral methods
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Abstract:This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. For this purpose, Hexic-kind Chebyshev polynomials (HCPs) are used as the backbone of the method to transform the primary problem into a set of nonlinear algebraic equations, which can be efficiently solved using numerical solvers, such as the Newton–Raphson method. The primary reason of choosing HCPs is due to their remarkable recurrence relations, facilitating their efficient computation and manipulation in mathematical analyses. A comprehensive convergence analysis was conducted to validate the robustness of the proposed method, with an error bound derived to provide theoretical guarantees for the solution’s accuracy. The method’s effectiveness is further demonstrated through two test examples, where the numerical results are compared with existing solutions, confirming the approach’s accuracy and reliability.
ISSN:2075-1680
DOI:10.3390/axioms14070515
Quelle:Engineering Database