Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction

Abdur Rashid; Shakaib Akram

Applications of Mathematics (2010)

  • Volume: 55, Issue: 4, page 337-350
  • ISSN: 0862-7940

Abstract

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In this paper, the evolution equations with nonlinear term describing the resonance interaction between the long wave and the short wave are studied. The semi-discrete and fully discrete Crank-Nicholson Fourier spectral schemes are given. An energy estimation method is used to obtain error estimates for the approximate solutions. The numerical results obtained are compared with exact solution and found to be in good agreement.

How to cite

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Rashid, Abdur, and Akram, Shakaib. "Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction." Applications of Mathematics 55.4 (2010): 337-350. <http://eudml.org/doc/37852>.

@article{Rashid2010,
abstract = {In this paper, the evolution equations with nonlinear term describing the resonance interaction between the long wave and the short wave are studied. The semi-discrete and fully discrete Crank-Nicholson Fourier spectral schemes are given. An energy estimation method is used to obtain error estimates for the approximate solutions. The numerical results obtained are compared with exact solution and found to be in good agreement.},
author = {Rashid, Abdur, Akram, Shakaib},
journal = {Applications of Mathematics},
keywords = {long-short wave interaction; Fourier spectral method; energy estimation method; semidiscretization; evolution equations; resonance interaction; Crank-Nicolson Fourier spectral schemes; error estimates; numerical results; long-short wave interaction; Fourier spectral method; energy estimation method; semidiscretization; evolution equations; resonance interaction; Crank-Nicolson Fourier spectral schemes; error estimates; numerical results},
language = {eng},
number = {4},
pages = {337-350},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction},
url = {http://eudml.org/doc/37852},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Rashid, Abdur
AU - Akram, Shakaib
TI - Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 337
EP - 350
AB - In this paper, the evolution equations with nonlinear term describing the resonance interaction between the long wave and the short wave are studied. The semi-discrete and fully discrete Crank-Nicholson Fourier spectral schemes are given. An energy estimation method is used to obtain error estimates for the approximate solutions. The numerical results obtained are compared with exact solution and found to be in good agreement.
LA - eng
KW - long-short wave interaction; Fourier spectral method; energy estimation method; semidiscretization; evolution equations; resonance interaction; Crank-Nicolson Fourier spectral schemes; error estimates; numerical results; long-short wave interaction; Fourier spectral method; energy estimation method; semidiscretization; evolution equations; resonance interaction; Crank-Nicolson Fourier spectral schemes; error estimates; numerical results
UR - http://eudml.org/doc/37852
ER -

References

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  7. Ma, Y. C., 10.1002/sapm1978593201, Stud. Appl. Math. 59 (1978), 201-221. (1978) Zbl0399.76028MR0521795DOI10.1002/sapm1978593201
  8. Nishikawa, K., Hojo, H., Mima, K., Ikezi, H., 10.1103/PhysRevLett.33.148, Phys. Rev. Lett. 33 (1974), 148-151. (1974) DOI10.1103/PhysRevLett.33.148
  9. Quarteroni, A., Valli, A., Numerical approximation of partial differential equations, Springer Series in Computational Mathematics Springer Berlin (1997). (1997) 
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  11. Yadong, S., 10.1016/j.chaos.2005.01.066, Chaos Solitons Fractals 26 (2005), 527-539. (2005) MR2143966DOI10.1016/j.chaos.2005.01.066
  12. Yajima, N., Oikawa, M., 10.1143/PTP.56.1719, Prog. Theor. Phys. 56 (1974), 1719-1739. (1974) MR0438980DOI10.1143/PTP.56.1719
  13. Yajima, N., Satsuma, J., 10.1143/PTP.62.370, Prog. Theor. Phys. 62 (1979), 370-37. (1979) DOI10.1143/PTP.62.370
  14. Zhang, F., Xinmin, X., Pseudospectral method for a class of system of LS wave interaction, Numer. Math. Nanjing 12 (1990), 199-214. (1990) MR1082717

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