메뉴 건너뛰기




Volumn 53, Issue 9-10, 2011, Pages 1865-1877

The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves

Author keywords

Chebyshev polynomials; Collocation method; Discrete Fourier series; Modified Korteweg de Vries (mKdV) equation; Ostrovsky equation; Quartic B spline

Indexed keywords

B-SPLINE; CHEBYSHEV POLYNOMIALS; COLLOCATION METHOD; DISCRETE FOURIER SERIES; MODIFIED KORTEWEG-DE VRIES (MKDV) EQUATION; OSTROVSKY EQUATION;

EID: 79951951623     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.01.011     Document Type: Article
Times cited : (60)

References (36)
  • 2
    • 0000401372 scopus 로고
    • Nonlinear internal waves in a rotating ocean
    • Ostrovsky L.A. Nonlinear internal waves in a rotating ocean. Okeanologia 1978, 18:181-191.
    • (1978) Okeanologia , vol.18 , pp. 181-191
    • Ostrovsky, L.A.1
  • 3
    • 0035879405 scopus 로고    scopus 로고
    • Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation
    • Chen G.U., Boyd J.P. Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation. Physica D 2001, 155:201-222.
    • (2001) Physica D , vol.155 , pp. 201-222
    • Chen, G.U.1    Boyd, J.P.2
  • 4
    • 27144447718 scopus 로고    scopus 로고
    • On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons
    • Stepanyants Y.A. On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons. Chaos Solitons Fractals 2006, 28:193-204.
    • (2006) Chaos Solitons Fractals , vol.28 , pp. 193-204
    • Stepanyants, Y.A.1
  • 5
    • 34249030634 scopus 로고    scopus 로고
    • Stability of solitary waves of a generalized Ostrovsky equation
    • Levandosky S., Liu Y. Stability of solitary waves of a generalized Ostrovsky equation. SIAM J. Math. Anal. 2006, 38:985-1011.
    • (2006) SIAM J. Math. Anal. , vol.38 , pp. 985-1011
    • Levandosky, S.1    Liu, Y.2
  • 6
    • 77950339045 scopus 로고    scopus 로고
    • Conservative numerical schemes for the Ostrovsky equation
    • Yaguchi T., Matsuo T., Sugihara M. Conservative numerical schemes for the Ostrovsky equation. J. Comput. Appl. Math. 2010, 234:1036-1048.
    • (2010) J. Comput. Appl. Math. , vol.234 , pp. 1036-1048
    • Yaguchi, T.1    Matsuo, T.2    Sugihara, M.3
  • 7
    • 32844473567 scopus 로고    scopus 로고
    • Local and global well-posedness for the Ostrovsky equation
    • Linares F., Milanes A. Local and global well-posedness for the Ostrovsky equation. J. Differential Equations 2006, 222:325-340.
    • (2006) J. Differential Equations , vol.222 , pp. 325-340
    • Linares, F.1    Milanes, A.2
  • 8
    • 1042290983 scopus 로고    scopus 로고
    • Cauchy problem for the Ostrovsky equation
    • Varlamov V., Liu Y. Cauchy problem for the Ostrovsky equation. Discrete Contin. Dyn. Syst. 2004, 10:731-753.
    • (2004) Discrete Contin. Dyn. Syst. , vol.10 , pp. 731-753
    • Varlamov, V.1    Liu, Y.2
  • 9
    • 0004643910 scopus 로고
    • Numerical solutions of some nonlinear dispersive wave equations
    • Hunter J.K. Numerical solutions of some nonlinear dispersive wave equations. Lectures Appl. Math. 1990, 26:301-316.
    • (1990) Lectures Appl. Math. , vol.26 , pp. 301-316
    • Hunter, J.K.1
  • 10
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedure for solving a problem arising in modeling and design of certain optoelectronic devices
    • Dehghan M. Finite difference procedure for solving a problem arising in modeling and design of certain optoelectronic devices. Math. Comput. Simulation 2006, 71:16-30.
    • (2006) Math. Comput. Simulation , vol.71 , pp. 16-30
    • Dehghan, M.1
  • 11
    • 34249009986 scopus 로고    scopus 로고
    • Numerical studies on nonlinear Schrodinger equations by spectral collocation method with preconditoning
    • Javidi M., Golbabai A. Numerical studies on nonlinear Schrodinger equations by spectral collocation method with preconditoning. J. Math. Anal. Applic. 2007, 333:1119-1127.
    • (2007) J. Math. Anal. Applic. , vol.333 , pp. 1119-1127
    • Javidi, M.1    Golbabai, A.2
  • 12
    • 0036466870 scopus 로고    scopus 로고
    • Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation
    • Boyd J.P., Chen G.U. Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation. Wave Motion 2002, 35:141-155.
    • (2002) Wave Motion , vol.35 , pp. 141-155
    • Boyd, J.P.1    Chen, G.U.2
  • 13
    • 43049139190 scopus 로고    scopus 로고
    • New exact travelling wave solutions for the Ostrovsky equation
    • Kangalgil F., Ayaz F. New exact travelling wave solutions for the Ostrovsky equation. Phys. Lett., A 2008, 372:1831-1835.
    • (2008) Phys. Lett., A , vol.372 , pp. 1831-1835
    • Kangalgil, F.1    Ayaz, F.2
  • 14
    • 77953585881 scopus 로고    scopus 로고
    • Magnetohydrodynamic flow of a Sisko fluid in annular. A numerical study
    • Khan M., Abbas Q., Duru K. Magnetohydrodynamic flow of a Sisko fluid in annular. A numerical study. Int. J. Numer. Methods Fluids 2010, 62:1169-1180.
    • (2010) Int. J. Numer. Methods Fluids , vol.62 , pp. 1169-1180
    • Khan, M.1    Abbas, Q.2    Duru, K.3
  • 15
    • 70449100716 scopus 로고    scopus 로고
    • A novel traveling wave solution for Ostrovsky equation using Exp-function method
    • Koroglu C., Ozis T. A novel traveling wave solution for Ostrovsky equation using Exp-function method. Comput. Math. Appl. 2009, 58:2142-2146.
    • (2009) Comput. Math. Appl. , vol.58 , pp. 2142-2146
    • Koroglu, C.1    Ozis, T.2
  • 16
    • 3042638045 scopus 로고    scopus 로고
    • Stability of solitary waves and weak solutions for the Ostrovsky equation
    • Liu Y. Stability of solitary waves and weak solutions for the Ostrovsky equation. J. Differential Equations 2004, 203:159-183.
    • (2004) J. Differential Equations , vol.203 , pp. 159-183
    • Liu, Y.1
  • 17
    • 23144446528 scopus 로고    scopus 로고
    • Solitary waves and fundamental solution for Ostrovsky equation
    • Varlamov V., Liu Y. Solitary waves and fundamental solution for Ostrovsky equation. Math. Comput. Simulation 2005, 69:567-579.
    • (2005) Math. Comput. Simulation , vol.69 , pp. 567-579
    • Varlamov, V.1    Liu, Y.2
  • 18
    • 33947327251 scopus 로고    scopus 로고
    • A travelling wave solution to the Ostrovsky equation
    • Yusufoglu E., Bekir A. A travelling wave solution to the Ostrovsky equation. Appl. Math. Comput. 2007, 186:256-260.
    • (2007) Appl. Math. Comput. , vol.186 , pp. 256-260
    • Yusufoglu, E.1    Bekir, A.2
  • 19
    • 77953323351 scopus 로고    scopus 로고
    • Solitary waves solutions for a generalized KdV-MKdV equation with variable coefficients
    • Triki H., Taha T.R., Wazwaz A.M. Solitary waves solutions for a generalized KdV-MKdV equation with variable coefficients. Math. Comput. Simulation 2010, 80:1867-1873.
    • (2010) Math. Comput. Simulation , vol.80 , pp. 1867-1873
    • Triki, H.1    Taha, T.R.2    Wazwaz, A.M.3
  • 20
    • 67649213967 scopus 로고    scopus 로고
    • Sub-ODE method and soliton solutions for the variable-coefficient mKdV equation
    • Triki H., Wazwaz A.M. Sub-ODE method and soliton solutions for the variable-coefficient mKdV equation. Appl. Math. Comput. 2009, 214:370-373.
    • (2009) Appl. Math. Comput. , vol.214 , pp. 370-373
    • Triki, H.1    Wazwaz, A.M.2
  • 21
    • 23344431783 scopus 로고    scopus 로고
    • The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations
    • Wazwaz A.M. The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations. Comput. Math. Applic. 2005, 49:1101-1112.
    • (2005) Comput. Math. Applic. , vol.49 , pp. 1101-1112
    • Wazwaz, A.M.1
  • 24
    • 31144457420 scopus 로고    scopus 로고
    • The calculation of integrals involving B-splines by means of recursion relations
    • Bhatti M., Bracken P. The calculation of integrals involving B-splines by means of recursion relations. Appl. Math. Comp. 2006, 172:91-100.
    • (2006) Appl. Math. Comp. , vol.172 , pp. 91-100
    • Bhatti, M.1    Bracken, P.2
  • 27
    • 0000530444 scopus 로고
    • Global properties of pseudospectral methods
    • Solomonoff A., Turkel E. Global properties of pseudospectral methods. J. Comput. Phys. 1989, 81:239-276.
    • (1989) J. Comput. Phys. , vol.81 , pp. 239-276
    • Solomonoff, A.1    Turkel, E.2
  • 28
    • 57749203983 scopus 로고    scopus 로고
    • Numerical solution of a mathematical model for capillary formation in tumor angiogensis via the tau method
    • Saadatmandi A., Dehghan M. Numerical solution of a mathematical model for capillary formation in tumor angiogensis via the tau method. Commun. Numer. Methods Engrg. 2008, 24:1467-1474.
    • (2008) Commun. Numer. Methods Engrg. , vol.24 , pp. 1467-1474
    • Saadatmandi, A.1    Dehghan, M.2
  • 29
    • 73449109560 scopus 로고    scopus 로고
    • Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method
    • Saadatmandi A., Dehghan M. Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method. Numer. Methods Partial Differential Equations 2010, 26:239-252.
    • (2010) Numer. Methods Partial Differential Equations , vol.26 , pp. 239-252
    • Saadatmandi, A.1    Dehghan, M.2
  • 31
    • 34548359104 scopus 로고    scopus 로고
    • A numerical method for KdV equation using collocation and radial basis functions
    • Dehghan M., Shokri A. A numerical method for KdV equation using collocation and radial basis functions. Nonlinear Dynamics 2007, 50:111-120.
    • (2007) Nonlinear Dynamics , vol.50 , pp. 111-120
    • Dehghan, M.1    Shokri, A.2
  • 33
    • 56149124076 scopus 로고    scopus 로고
    • A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
    • Dehghan M., Shokri A. A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions. Mathematics and Computers in Simulation 2008, 79:700-715.
    • (2008) Mathematics and Computers in Simulation , vol.79 , pp. 700-715
    • Dehghan, M.1    Shokri, A.2
  • 34
    • 33749559910 scopus 로고    scopus 로고
    • The one-dimensional heat equation subject to a boundary integral specification
    • Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos, Solitons and Fractals 2007, 32:661-675.
    • (2007) Chaos, Solitons and Fractals , vol.32 , pp. 661-675
    • Dehghan, M.1
  • 35
    • 11144275388 scopus 로고    scopus 로고
    • On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation
    • Dehghan M. On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numerical Methods for Partial Differential Equations 2005, 21:24-40.
    • (2005) Numerical Methods for Partial Differential Equations , vol.21 , pp. 24-40
    • Dehghan, M.1
  • 36
    • 78049468429 scopus 로고    scopus 로고
    • A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
    • Shakeri F., Dehghan M. A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations. Applied Numerical Mathematics 2011, 61:1-23.
    • (2011) Applied Numerical Mathematics , vol.61 , pp. 1-23
    • Shakeri, F.1    Dehghan, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.