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

Kamel Al-Khaled

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)234-250
Number of pages17
JournalAnnals of the University of Craiova, Mathematics and Computer Science Series
Volume41
Issue number2
Publication statusPublished - 2014

Fingerprint

Fractional Derivative
Legendre
Collocation Method
Fractional
Sinc Method
Derivatives
Legendre polynomial
Burgers Equation
Traffic Flow
Collocation
Time Domain
Approximate Solution
Exact Solution
Polynomials
Numerical Solution
Entire
Valid
Converge
Numerical Results
Approximation

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

Cite this

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

In: Annals of the University of Craiova, Mathematics and Computer Science Series, Vol. 41, No. 2, 2014, p. 234-250.

Research output: Contribution to journalArticle

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