Numerical computation of water and solitary waves by the double exponential transform

Journal of Computational and Applied Mathematics

Volumn 152, Issue 1-2, 2003, Pages 229-241

  Kobayashi, K ^a   Okamoto, H ^a   Zhu, J ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Double exponential transform; Nekrasov's integral equation; Yamada's integral equation

Indexed keywords

FAST FOURIER TRANSFORMS; INTEGRAL EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

SOLITARY WAVES;

WATER WAVES;

MATHEMATICAL ANALYSIS; SOLITARY WAVE; WATER WAVE;

EID: 0037334674     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00708-2     Document Type: Article

References (9)

1. C.J. Amick, L.E. Fraenkel, On the behavior near the crest of waves of extreme form, Trans. Amer. Math. Soc. 299 (1987) 273-298.
2. G.A. Chandler, I.G. Graham, The computation of water waves modelled by Nekrasov's equation, SIAM J. Numer. Anal. 30 (1993) 1041-1065.
3. K. Kobayashi, Computation of simultaneous integration by the DE transform and FFT and its application to integral equations, Proceedings of the Annual Meeting of the Applied Mathematics by JSPS Research Grants, 1999, pp. 125-128 (in Japanese).
4. K. Kobayashi, H. Okamoto, J. Zhu, High-accuracy computation of gravity waves via DE transform and FFT, Proceedings of the Annual Meeting of the Applied Mathematics by JSPS Research Grants, 2000, pp.95-98 (in Japanese).
5. H. Okamoto, M. Shöji, The Mathematical Theory of Permanent Progressive Water-Waves, World Scientific Publ. Co., Singapore, 2001.
6. F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer, Berlin, 1993.
7. M. Sugihara, Optimality of the double exponential formula-functional analysis approach, Numer. Math. 75 (1997) 379-395.
8. H. Takahasi, M. Mori, Double exponential formulas for numerical integration, Publ. Res. Inst. Math. Soc. 9 (1974) 721-741.
9. N. Tiangtae, H. Sugiura, Legendre-Galerkin method for Poisson equation on a fan-shaped domain, Trans. Japan Soc. Indust. Appl. Math. 11 (2001) 27-40 (in Japanese).