### Abstract

In this Letter we present an Adomian's decomposition Method (shortly ADM) and the Sinc-Galerkin Method (shortly SGM) for numerical approximation traveling wave solutions of the Kawahara equation. We obtain the exact traveling wave solutions of the Kawahara equation for the initial conditions by using ADM. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions.

Original language | English |
---|---|

Pages (from-to) | 433-439 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 363 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Apr 9 2007 |

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### Keywords

- Adomian decomposition method
- Kawahara equation
- Sinc-Galerkin method
- Traveling wave solution

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*363*(5-6), 433-439. https://doi.org/10.1016/j.physleta.2006.11.055

**A numerical comparison of a Kawahara equation.** / Kaya, Doǧan; Al-Khaled, Kamel.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 363, no. 5-6, pp. 433-439. https://doi.org/10.1016/j.physleta.2006.11.055

}

TY - JOUR

T1 - A numerical comparison of a Kawahara equation

AU - Kaya, Doǧan

AU - Al-Khaled, Kamel

PY - 2007/4/9

Y1 - 2007/4/9

N2 - In this Letter we present an Adomian's decomposition Method (shortly ADM) and the Sinc-Galerkin Method (shortly SGM) for numerical approximation traveling wave solutions of the Kawahara equation. We obtain the exact traveling wave solutions of the Kawahara equation for the initial conditions by using ADM. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions.

AB - In this Letter we present an Adomian's decomposition Method (shortly ADM) and the Sinc-Galerkin Method (shortly SGM) for numerical approximation traveling wave solutions of the Kawahara equation. We obtain the exact traveling wave solutions of the Kawahara equation for the initial conditions by using ADM. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions.

KW - Adomian decomposition method

KW - Kawahara equation

KW - Sinc-Galerkin method

KW - Traveling wave solution

UR - http://www.scopus.com/inward/record.url?scp=33847056255&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847056255&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2006.11.055

DO - 10.1016/j.physleta.2006.11.055

M3 - Article

AN - SCOPUS:33847056255

VL - 363

SP - 433

EP - 439

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 5-6

ER -