Spectral collocation solution of a generalized Hirota–Satsuma coupled KdV equation

References

• Wu , Y. T. , Geng , X. G. , Hu , X. B. and Zhu , S. M. 1999 . A generalized Hirota–Satsuma coupled Korteweg–de Vries equation and Miura transformations . Physics Letters A , 255 : 259 – 264 .
   Web of Science ®Google Scholar
• Hirota , R. and Satsuma , J. 1981 . Soliton solution of a coupled Korteweg–de Vries equation . Physics Letters A , 85 : 407 – 408 .
   Web of Science ®Google Scholar
• Fan , E. 2001 . Soliton solutions for generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation . Physics Letters A , 282 : 18 – 22 .
   Web of Science ®Google Scholar
• Kaya , D. 2004 . Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation . Applied Mathematics and Computation , 147 : 69 – 78 .
   Web of Science ®Google Scholar
• Gottlieb , D. , Hussaini , M. Y. and Orszag , S. A. 1984 . “ Theory and application of spectral methods ” . In Spectral Methods for Partial Differential Equations , Edited by: Voigt , R. G. , Gottlieb , D. and Hussaini , M. Y. 1 – 54 . Philadelphia : SIAM-CBMS .
   Google Scholar
• Solomonoff , A. and Turkel , E. 1989 . Global properties of pseudospectral methods . Journal of Computational Physics , 81 : 239 – 276 .
   Web of Science ®Google Scholar
• Don , W. S. and Solomonoff , A. 1995 . Accuracy and speed in computing the Chebyshev collocation derivative . SIAM Journal on Scientific Computing , 16 : 1253 – 1268 .
   Web of Science ®Google Scholar
• Don , W. S. and Solomonoff , A. 1997 . Accuracy enhancement for higher derivatives using Chebyshev collocation and a mapping technique . SIAM Journal on Scientific Computing , 18 : 1040 – 1055 .
   Web of Science ®Google Scholar
• Baltensperger , R. and Berrut , J. P. 1999 . The errors in calculating the pseudospetral differentiation matrices for Chebvshev–Gauss–Lobatto points . Computers and Mathematics with Applications , 37 : 41 – 48 .
   Web of Science ®Google Scholar
• Baltensperger , R. and Trummer , M. R. 2003 . Spectral differencing with a twist . SIAM Journal on Scientific Computing , 24 : 1465 – 1487 .
   Web of Science ®Google Scholar
• Bayliss , A. , Class , A. and Matkowsky , B. 1995 . Roundoff error in computing derivatives using the Chebyshev differentiation matrix . Journal of Computational Physics , 116 : 380 – 383 .
   Web of Science ®Google Scholar
• Breuer , K. S. and Everson , R. S. 1992 . On the errors incurred calculating derivatives using Chebyshev polynomials . Journal of Computational Physics , 99 : 56 – 67 .
   Web of Science ®Google Scholar
• Rothman , E. E. 1991 . “ Reducing round-off error in Chebyshev pseudospectral computations ” . In High Performance Computing II , Edited by: Durant , M. and El Dabaghi , F. 423 – 439 . Amsterdam : Elsevier–North-Holland .
   Google Scholar
• Tang , T. and Trummer , M. R. 1996 . Boundary layer resolving pseudospectral methods for singular perturbation problems . SIAM Journal on Scientific Computing Physics , 17 : 430 – 438 .
   Web of Science ®Google Scholar
• Darvishi , M. T. and Ghoreishi , F. 1999 . Error reduction for higher derivatives of Chebyshev collocation method using preconditioning and domain decomposition . Korean Journal of Computational and Applied Mathematics , 6 : 421 – 435 .
   Google Scholar
• Darvishi , M. T. 2004 . Preconditioning and domain decomposition schemes to solve PDEs . International Journal of Pure and Applied Mathematics , 1 : 419 – 439 .
   Google Scholar
• Young , D. M. 1971 . Iterative Solution of Large Linear Systems , New York : Academic Press .
   Google Scholar
• DeVogelaere , R. 1985 . Over-relaxations . Abstract No. 539-553, Amer. Math. Soc., Notices 5, (147)
   Google Scholar