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 |
|---|---|
| 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
Rigorous computation of Nekrasov’s integral equation for water waves. / Murashige, Sunao; Oishi, Shinichi.
Advances in Engineering Mechanics Reflections and Outlooks: In Honor of Theodore Y-T Wu. World Scientific Publishing Co., 2005. p. 84-93.Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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
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 -