### Abstract

This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method.

Original language | English |
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Pages (from-to) | 441-452 |

Number of pages | 12 |

Journal | Applications of Mathematics |

Volume | 59 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- advection-diffusion equation
- numerical solution
- Sinc-Galerkin method

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods.** / Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Applications of Mathematics*, vol. 59, no. 4, pp. 441-452. https://doi.org/10.1007/s10492-014-0065-3

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TY - JOUR

T1 - Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods

AU - Al-Khaled, Kamel

PY - 2014

Y1 - 2014

N2 - This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method.

AB - This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method.

KW - advection-diffusion equation

KW - numerical solution

KW - Sinc-Galerkin method

UR - http://www.scopus.com/inward/record.url?scp=84904735065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904735065&partnerID=8YFLogxK

U2 - 10.1007/s10492-014-0065-3

DO - 10.1007/s10492-014-0065-3

M3 - Article

AN - SCOPUS:84904735065

VL - 59

SP - 441

EP - 452

JO - Applications of Mathematics

JF - Applications of Mathematics

SN - 0862-7940

IS - 4

ER -