### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

*Journal of Computational and Applied Mathematics*,

*130*(1-2), 283-292.

**Sine numerical solution for solitons and solitary waves.** / Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 130, no. 1-2, pp. 283-292.

}

TY - JOUR

T1 - Sine numerical solution for solitons and solitary waves

AU - Al-Khaled, Kamel

PY - 2001/5/1

Y1 - 2001/5/1

N2 - 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.

AB - 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.

KW - Korteweg-de Vries equation

KW - Pulse solution

KW - Sine function

UR - http://www.scopus.com/inward/record.url?scp=0035338865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035338865&partnerID=8YFLogxK

M3 - Article

VL - 130

SP - 283

EP - 292

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -