### 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 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics