Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative

Autor: Harvindra Singh, A. K. Mittal, L. K. Balyan
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Arabian Journal of Mathematics, Vol 13, Iss 2, Pp 409-424 (2024)
Druh dokumentu: article
ISSN: 2193-5343
2193-5351
DOI: 10.1007/s40065-024-00465-0
Popis: Abstract This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of $$ \nu $$ ν is done for various model examples of fractional Burgers equations, where $$\nu $$ ν represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.
Databáze: Directory of Open Access Journals
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