Cubic spline based differential quadrature method: A numerical approach for fractional Burger equation
In this research paper, our main objective is to represent a direct numerical approach for solving time-fractional Burger’s equation using modified hybrid B-spline basis function. The Caputo derivative is used to discretize the time-fractional derivative and for Space derivative Differential Quadrat...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-07-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379721005362 |
| Summary: | In this research paper, our main objective is to represent a direct numerical approach for solving time-fractional Burger’s equation using modified hybrid B-spline basis function. The Caputo derivative is used to discretize the time-fractional derivative and for Space derivative Differential Quadrature Method (DQM) based on B-Spline is used. The DQM method has its own inherited advantage being a simple and programable method. The embedding of B-spline basis makes it more practical to approximate the solution curve. DQM with B-spline basis is a simple and efficient technique based on the matrix approach. The problem is discretized in the system of non-linear equations and then further solved by a programming tools. The stability is examined by the matrix-based approach. The presented method has been applied to three test problems. The obtained results showed that the proposed method is good for solving non-linear time-fractional Burger’s equation. The approximated solutions are graphically represented and the results showed that solutions are closed to the exact solution. |
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| ISSN: | 2211-3797 |