### Abstract

A numerical scheme using Sine-Galerkin method is developed to approximate the solution for the Korteweg-de Vries model equation. Sine approximation to both derivatives and indefinite integral reduce the integral equation to an explicit system of algebraic equations, then using various properties of Sine functions, it is shown that the Sine solution produce an error of order script O sign(exp(-c/h)) for some positive constants c, h. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

Original language | English |
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Pages (from-to) | 283-292 |

Number of pages | 10 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 130 |

Issue number | 1-2 |

Publication status | Published - May 1 2001 |

### Keywords

- Korteweg-de Vries equation
- Pulse solution
- Sine function

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

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## Cite this

Al-Khaled, K. (2001). Sine numerical solution for solitons and solitary waves.

*Journal of Computational and Applied Mathematics*,*130*(1-2), 283-292.