### Abstract

Nekrasov’s integral equation is a mathematical model for two-dimensional, periodic, symmetric and progressive waves on the surface of water. Although some iterative numerical methods have been developed for this type of integral equation, high dimensional approximation is required for the case of large wave height. This paper proposes the method of error estimate for this problem using a numerical verification technique based on a fixed point theorem and interval analysis. This method enables us to show existence of exact solutions in a neighborhood of an approximate solution.

Original language | English |
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Title of host publication | Advances in Engineering Mechanics Reflections and Outlooks: In Honor of Theodore Y-T Wu |

Publisher | World Scientific Publishing Co. |

Pages | 84-93 |

Number of pages | 10 |

ISBN (Print) | 9789812702128, 9812561447, 9789812561442 |

DOIs | |

Publication status | Published - 2005 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Advances in Engineering Mechanics Reflections and Outlooks: In Honor of Theodore Y-T Wu*(pp. 84-93). World Scientific Publishing Co.. https://doi.org/10.1142/9789812702128_0006

**Rigorous computation of Nekrasov’s integral equation for water waves.** / Murashige, Sunao; Oishi, Shinichi.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Engineering Mechanics Reflections and Outlooks: In Honor of Theodore Y-T Wu.*World Scientific Publishing Co., pp. 84-93. https://doi.org/10.1142/9789812702128_0006

}

TY - CHAP

T1 - Rigorous computation of Nekrasov’s integral equation for water waves

AU - Murashige, Sunao

AU - Oishi, Shinichi

PY - 2005/1/1

Y1 - 2005/1/1

N2 - Nekrasov’s integral equation is a mathematical model for two-dimensional, periodic, symmetric and progressive waves on the surface of water. Although some iterative numerical methods have been developed for this type of integral equation, high dimensional approximation is required for the case of large wave height. This paper proposes the method of error estimate for this problem using a numerical verification technique based on a fixed point theorem and interval analysis. This method enables us to show existence of exact solutions in a neighborhood of an approximate solution.

AB - Nekrasov’s integral equation is a mathematical model for two-dimensional, periodic, symmetric and progressive waves on the surface of water. Although some iterative numerical methods have been developed for this type of integral equation, high dimensional approximation is required for the case of large wave height. This paper proposes the method of error estimate for this problem using a numerical verification technique based on a fixed point theorem and interval analysis. This method enables us to show existence of exact solutions in a neighborhood of an approximate solution.

UR - http://www.scopus.com/inward/record.url?scp=84967496037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84967496037&partnerID=8YFLogxK

U2 - 10.1142/9789812702128_0006

DO - 10.1142/9789812702128_0006

M3 - Chapter

AN - SCOPUS:84967496037

SN - 9789812702128

SN - 9812561447

SN - 9789812561442

SP - 84

EP - 93

BT - Advances in Engineering Mechanics Reflections and Outlooks: In Honor of Theodore Y-T Wu

PB - World Scientific Publishing Co.

ER -