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

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 d...

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Bibliographic Details
Published in:Arabian journal of mathematics 2024-08, Vol.13 (2), p.409-424
Main Authors: Singh, Harvindra, Mittal, A. K., Balyan, L. K.
Format: Article
Language:English
Subjects:
35C11
35G31
35R11
65M70
Burgers equation
Chebyshev approximation
Error analysis
Exact solutions
Finite volume method
Mathematics
Mathematics and Statistics
Nonlinear equations
Partial differential equations
Reynolds number
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Summary: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 ν is done for various model examples of fractional Burgers equations, where ν represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.
ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-024-00465-0