### Abstract

This paper deals with the numerical solution of the nonlinear fractional Burgers' equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The solution is based on using the Sinc method, which builds an approximate solution valid on the entire spatial domain, and in the time domain, we use the shifted Legendre polynomials to replace the time fractional derivatives. The error in the approximation is shown to converge to the exact solution at an exponential rate. Illustrative examples are given with an applications from traffic flow, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

Original language | English |
---|---|

Pages (from-to) | 234-250 |

Number of pages | 17 |

Journal | Annals of the University of Craiova, Mathematics and Computer Science Series |

Volume | 41 |

Issue number | 2 |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Burgers equation
- Fractional derivative
- Numerical solutions
- Shifted-legendre polynomials
- Sinc-collocation

### ASJC Scopus subject areas

- Mathematics(all)
- Computer Science Applications

### Cite this

*Annals of the University of Craiova, Mathematics and Computer Science Series*,

*41*(2), 234-250.

**Sinc-Legendre collocation method for the non-linear Burgers' fractional equation.** / Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Annals of the University of Craiova, Mathematics and Computer Science Series*, vol. 41, no. 2, pp. 234-250.

}

TY - JOUR

T1 - Sinc-Legendre collocation method for the non-linear Burgers' fractional equation

AU - Al-Khaled, Kamel

PY - 2014

Y1 - 2014

N2 - This paper deals with the numerical solution of the nonlinear fractional Burgers' equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The solution is based on using the Sinc method, which builds an approximate solution valid on the entire spatial domain, and in the time domain, we use the shifted Legendre polynomials to replace the time fractional derivatives. The error in the approximation is shown to converge to the exact solution at an exponential rate. Illustrative examples are given with an applications from traffic flow, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

AB - This paper deals with the numerical solution of the nonlinear fractional Burgers' equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The solution is based on using the Sinc method, which builds an approximate solution valid on the entire spatial domain, and in the time domain, we use the shifted Legendre polynomials to replace the time fractional derivatives. The error in the approximation is shown to converge to the exact solution at an exponential rate. Illustrative examples are given with an applications from traffic flow, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

KW - Burgers equation

KW - Fractional derivative

KW - Numerical solutions

KW - Shifted-legendre polynomials

KW - Sinc-collocation

UR - http://www.scopus.com/inward/record.url?scp=84920287179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920287179&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84920287179

VL - 41

SP - 234

EP - 250

JO - Annals of the University of Craiova, Mathematics and Computer Science Series

JF - Annals of the University of Craiova, Mathematics and Computer Science Series

SN - 1223-6934

IS - 2

ER -