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Volumn 39, Issue 2, 2009, Pages 849-857

A new domain decomposition algorithm for generalized Burger's-Huxley equation based on Chebyshev polynomials and preconditioning

Author keywords

[No Author keywords available]

Indexed keywords

DOMAIN DECOMPOSITION METHODS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIALS;

EID: 62749121611     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.01.099     Document Type: Article
Times cited : (60)

References (37)
  • 1
    • 4944259773 scopus 로고    scopus 로고
    • Adomian decomposition method for Burger's Huxley and Burger's-Fisher equations
    • Ismail H.N.A., Raslan K., and Rabboh A.A.A. Adomian decomposition method for Burger's Huxley and Burger's-Fisher equations. Appl Math Comput 159 (2004) 291-301
    • (2004) Appl Math Comput , vol.159 , pp. 291-301
    • Ismail, H.N.A.1    Raslan, K.2    Rabboh, A.A.A.3
  • 2
    • 0038227457 scopus 로고
    • Solitary wave solutions of the generalized Burger's-Huxley equation
    • Printed in the UK
    • Wang X.Y., Zhu Z.S., and Lu Y.K. Solitary wave solutions of the generalized Burger's-Huxley equation. J Phys A: Math Gen 23 (1990) 271-274 Printed in the UK
    • (1990) J Phys A: Math Gen , vol.23 , pp. 271-274
    • Wang, X.Y.1    Zhu, Z.S.2    Lu, Y.K.3
  • 3
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • Hodgkin A.L., and Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117 (1952) 500-544
    • (1952) J Physiol , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 4
    • 0002721581 scopus 로고
    • Mathematical models of excitation and propagation in nerve
    • Schwan H.P. (Ed), McGraw-Hill, Nyork
    • Fitzhugh R. Mathematical models of excitation and propagation in nerve. In: Schwan H.P. (Ed). Biological engineering (1969), McGraw-Hill, Nyork 1-85
    • (1969) Biological engineering , pp. 1-85
    • Fitzhugh, R.1
  • 5
    • 21344476543 scopus 로고
    • Non-classical symmetries and the singular modified the Burger's and Burger's-Huxley equation
    • Estevez P.G. Non-classical symmetries and the singular modified the Burger's and Burger's-Huxley equation. J Phys A 27 (1994) 2113-2127
    • (1994) J Phys A , vol.27 , pp. 2113-2127
    • Estevez, P.G.1
  • 6
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons Fract 26 3 (2005) 695-700
    • (2005) Chaos Solitons Fract , vol.26 , Issue.3 , pp. 695-700
    • He, J.H.1
  • 7
    • 18844391045 scopus 로고    scopus 로고
    • Limit cycle and bifurcation of nonlinear problems
    • He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos Solitons Fract 26 3 (2005) 827-833
    • (2005) Chaos Solitons Fract , vol.26 , Issue.3 , pp. 827-833
    • He, J.H.1
  • 8
    • 17844395724 scopus 로고    scopus 로고
    • Application of He's homotopy perturbation method to volterra's integro-differential equation
    • El-Shahed M. Application of He's homotopy perturbation method to volterra's integro-differential equation. Chaos Solitons Fract 6 2 (2005) 163-168
    • (2005) Chaos Solitons Fract , vol.6 , Issue.2 , pp. 163-168
    • El-Shahed, M.1
  • 9
    • 0032308350 scopus 로고    scopus 로고
    • Approximate solution of nonlinear differential equations with convolution product nonlinearities
    • He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput Meth Appl Mech Eng 167 1-2 (1998) 69-73
    • (1998) Comput Meth Appl Mech Eng , vol.167 , Issue.1-2 , pp. 69-73
    • He, J.H.1
  • 10
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Meth Appl Mech Eng 167 1-2 (1998) 57-68
    • (1998) Comput Meth Appl Mech Eng , vol.167 , Issue.1-2 , pp. 57-68
    • He, J.H.1
  • 11
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration methoda kind of non-linear analytical technique: some examples
    • He J.H. Variational iteration methoda kind of non-linear analytical technique: some examples. Int J Non-Linear Mech 34 4 (1999) 699-708
    • (1999) Int J Non-Linear Mech , vol.34 , Issue.4 , pp. 699-708
    • He, J.H.1
  • 12
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for autonomous ordinary differential systems
    • He J.H. Variational iteration method for autonomous ordinary differential systems. Appl Math Comput 114 2-3 (2000) 115-123
    • (2000) Appl Math Comput , vol.114 , Issue.2-3 , pp. 115-123
    • He, J.H.1
  • 13
    • 24944474278 scopus 로고    scopus 로고
    • Application of He's variational iteration method to Helmholtz equation
    • Momani S., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos Solitons Fract 27 5 (2006) 1119-1123
    • (2006) Chaos Solitons Fract , vol.27 , Issue.5 , pp. 1119-1123
    • Momani, S.1    Abuasad, S.2
  • 14
    • 31444443560 scopus 로고    scopus 로고
    • A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations
    • Soliman A.A. A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations. Chaos Solitons Fract 29 2 (2006) 294-302
    • (2006) Chaos Solitons Fract , vol.29 , Issue.2 , pp. 294-302
    • Soliman, A.A.1
  • 15
    • 31444453811 scopus 로고    scopus 로고
    • The solution of nonlinear coagulation problem with mass loss
    • Abulwafa E.M., Abdou M.A., and Mahmoud A.A. The solution of nonlinear coagulation problem with mass loss. Chaos Solitons Fract 29 2 (2006) 313-330
    • (2006) Chaos Solitons Fract , vol.29 , Issue.2 , pp. 313-330
    • Abulwafa, E.M.1    Abdou, M.A.2    Mahmoud, A.A.3
  • 16
    • 30344464250 scopus 로고    scopus 로고
    • Application of variational iteration method to nonlinear differential equations of fractional order
    • Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int J Nonlinear Sci Numer Simulat 7 1 (2006) 27-36
    • (2006) Int J Nonlinear Sci Numer Simulat , vol.7 , Issue.1 , pp. 27-36
    • Odibat, Z.M.1    Momani, S.2
  • 17
    • 35348928017 scopus 로고    scopus 로고
    • Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method
    • Javidi M., and Golbabai A. Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method. Chaos Solitons Fract 36 2 (2008) 309-313
    • (2008) Chaos Solitons Fract , vol.36 , Issue.2 , pp. 309-313
    • Javidi, M.1    Golbabai, A.2
  • 18
    • 38649095232 scopus 로고    scopus 로고
    • Exact solitary wave solution of Boussinesq equation by VIM
    • Javidi M., and Jalilian Y. Exact solitary wave solution of Boussinesq equation by VIM. Chaos Solitons Fract 36 5 (2008) 1256-1260
    • (2008) Chaos Solitons Fract , vol.36 , Issue.5 , pp. 1256-1260
    • Javidi, M.1    Jalilian, Y.2
  • 19
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He J.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fract 30 3 (2006) 700-708
    • (2006) Chaos Solitons Fract , vol.30 , Issue.3 , pp. 700-708
    • He, J.H.1
  • 20
    • 34250163508 scopus 로고    scopus 로고
    • New periodic solutions for nonlinear evolution equations using Exp-function method
    • He J.H., and Abdou M.A. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Solitons Fract 34 5 (2007) 1421-1429
    • (2007) Chaos Solitons Fract , vol.34 , Issue.5 , pp. 1421-1429
    • He, J.H.1    Abdou, M.A.2
  • 21
    • 13444310842 scopus 로고    scopus 로고
    • Applications of F-expansion to periodicwave solutions of a new Hamiltonian amplitude equation
    • Wang M., and Li X. Applications of F-expansion to periodicwave solutions of a new Hamiltonian amplitude equation. Chaos Solitons Fract 24 5 (2005) 1257-1268
    • (2005) Chaos Solitons Fract , vol.24 , Issue.5 , pp. 1257-1268
    • Wang, M.1    Li, X.2
  • 22
  • 23
    • 0036283904 scopus 로고    scopus 로고
    • An approximate solution for one-dimensional weakly nonlinear oscillations
    • Marinca V. An approximate solution for one-dimensional weakly nonlinear oscillations. Int J Nonlinear Sci Numer Simulat 3 2 (2002) 107-120
    • (2002) Int J Nonlinear Sci Numer Simulat , vol.3 , Issue.2 , pp. 107-120
    • Marinca, V.1
  • 24
    • 0032761614 scopus 로고    scopus 로고
    • The errors in calculating the pseudospectral differentiation matrices for Chebyshev-Gauss-Lobatto point
    • Baltensperger R., and Berrut J.P. The errors in calculating the pseudospectral differentiation matrices for Chebyshev-Gauss-Lobatto point. Comput Math Appl 37 (1999) 41-48
    • (1999) Comput Math Appl , vol.37 , pp. 41-48
    • Baltensperger, R.1    Berrut, J.P.2
  • 25
    • 0141975242 scopus 로고    scopus 로고
    • Spectral differencing with a twist
    • Baltenperger R., and Trummer M.R. Spectral differencing with a twist. SIAM J Sci Comput 24 5 (2003) 1465-1487
    • (2003) SIAM J Sci Comput , vol.24 , Issue.5 , pp. 1465-1487
    • Baltenperger, R.1    Trummer, M.R.2
  • 26
    • 0003210689 scopus 로고
    • Chebyshev and Fourier spectral methods
    • Springer, verlag, Berlin
    • Boyd J.P. Chebyshev and Fourier spectral methods. Lecture notes in engineering vol. 49 (1989), Springer, verlag, Berlin
    • (1989) Lecture notes in engineering , vol.49
    • Boyd, J.P.1
  • 28
    • 0001044964 scopus 로고
    • Accuracy and speed in computing the Chebyshev collocation derivative
    • Don W.S., and Solomonoff A. Accuracy and speed in computing the Chebyshev collocation derivative. SIAM J Sci Comput 16 4 (1995) 1253-1268
    • (1995) SIAM J Sci Comput , vol.16 , Issue.4 , pp. 1253-1268
    • Don, W.S.1    Solomonoff, A.2
  • 30
    • 0001096265 scopus 로고
    • Roundoff error in computing derivatives using the Chebyshev differentiation matrix
    • Bayliss A., Class A., and Matkowsky B.J. Roundoff error in computing derivatives using the Chebyshev differentiation matrix. J Comput Phys 116 (1995) 380-383
    • (1995) J Comput Phys , vol.116 , pp. 380-383
    • Bayliss, A.1    Class, A.2    Matkowsky, B.J.3
  • 31
    • 84966247397 scopus 로고
    • Generation of finite difference formulas on arbitarily spaced grids
    • Fornberg B. Generation of finite difference formulas on arbitarily spaced grids. Math Comput 51 (1988) 699-706
    • (1988) Math Comput , vol.51 , pp. 699-706
    • Fornberg, B.1
  • 32
    • 0000603224 scopus 로고    scopus 로고
    • A MATLAB differentiation matrix suite
    • Weideman J.A.C., and Reddy S.C. A MATLAB differentiation matrix suite. Trans Math Software 26 (2000) 465-519
    • (2000) Trans Math Software , vol.26 , pp. 465-519
    • Weideman, J.A.C.1    Reddy, S.C.2
  • 33
    • 0001216115 scopus 로고
    • Generation of pseudospectral differentiation matrices, I
    • Welfert B.D. Generation of pseudospectral differentiation matrices, I. SIAM J Numer Anal 34 (1977) 1640-1657
    • (1977) SIAM J Numer Anal , vol.34 , pp. 1640-1657
    • Welfert, B.D.1
  • 34
    • 0000530444 scopus 로고
    • Global properties of pseudospectral methods
    • Solomonoff A., and Turkel E. Global properties of pseudospectral methods. J Comput Phys 81 (1989) 239-276
    • (1989) J Comput Phys , vol.81 , pp. 239-276
    • Solomonoff, A.1    Turkel, E.2
  • 35
    • 0022662366 scopus 로고
    • Spectral methods in time for hyperbolic equations
    • Tal-Ezer H. Spectral methods in time for hyperbolic equations. SIAM J Numer Anal 23 1 (1986) 11-26
    • (1986) SIAM J Numer Anal , vol.23 , Issue.1 , pp. 11-26
    • Tal-Ezer, H.1
  • 36
    • 32144460893 scopus 로고    scopus 로고
    • Preconditioning and domain decomposition scheme to solve PDEs
    • Darvishi M.T. Preconditioning and domain decomposition scheme to solve PDEs. Int J Pure Appl Math 15 4 (2004) 419-439
    • (2004) Int J Pure Appl Math , vol.15 , Issue.4 , pp. 419-439
    • Darvishi, M.T.1
  • 37
    • 32144444944 scopus 로고    scopus 로고
    • Error reduction for higher derivatives of Chebyshev collocation method using preconditioning and domain decomposition
    • Darvishi M.T., and Ghoreishi F. Error reduction for higher derivatives of Chebyshev collocation method using preconditioning and domain decomposition. Korean J Comput Appl Math 6 2 (1999) 421-435
    • (1999) Korean J Comput Appl Math , vol.6 , Issue.2 , pp. 421-435
    • Darvishi, M.T.1    Ghoreishi, F.2


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