Blow-up solutions obtained using the decomposition method

This paper deals with obtaining explicit solutions of a generalised non-linear Boussinesq equation using the Adomian decomposition method. Both finite and blow-up solutions can be obtained.

[1]  H.-W. Choi,et al.  Symbolic implementation of the algorithm for calculating Adomian polynomials , 2003, Appl. Math. Comput..

[2]  G. J. Collins,et al.  An asymptotic and numerical description of self-similar blow-up in quasilinear parabolic equations , 1998 .

[3]  Peter S. Lomdahl,et al.  On a Toda lattice model with a transversal degree of freedom , 1991 .

[4]  Shijun Liao,et al.  A new analytic algorithm of Lane-Emden type equations , 2003, Appl. Math. Comput..

[5]  Yoshikazu Giga,et al.  Nonlinear Partial Differential Equations , 2004 .

[6]  G. Adomian,et al.  Noise terms in decomposition solution series , 1992 .

[7]  Solitary waves on nonlinear elastic rods. I , 1984 .

[8]  Randolph Rach,et al.  A convenient computational form for the Adomian polynomials , 1984 .

[9]  G. F. Roach,et al.  Adomian's method for Hammerstein integral equations arising from chemical reactor theory , 2001, Appl. Math. Comput..

[10]  H. Bilz,et al.  Solitary Wave Solutions in a Diatomic Lattice , 1978 .

[11]  Jianhong Wu,et al.  Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation , 2000, Appl. Math. Comput..

[12]  G. Adomian A review of the decomposition method in applied mathematics , 1988 .

[13]  G. Adomian Solution of coupled nonlinear partial differential equations by decomposition , 1996 .

[14]  Y. Cherruault,et al.  Convergence of Adomian's method applied to differential equations , 1994 .

[15]  A. Wazwaz Necessary conditions for the appearance of noise terms in decomposition solutions series , 1997 .

[16]  Muhammad Aslam Noor,et al.  Numerical comparison of methods for solving parabolic equations , 2004, Appl. Math. Comput..

[17]  Y. Cherruault,et al.  Decomposition methods: A new proof of convergence , 1993 .

[18]  George Adomian,et al.  Generalization of adomian polynomials to functions of several variables , 1992 .

[19]  Abdul-Majid Wazwaz Blow-up for solutions of some linear wave equations with mixed nonlinear boundary conditions , 2001, Appl. Math. Comput..

[20]  Hermann Brunner,et al.  Blowup in diffusion equations: a survey , 1998 .

[21]  L. Gabet,et al.  The theoretical foundation of the Adomian method , 1994 .

[22]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[23]  Abdul-Majid Wazwaz,et al.  A new algorithm for calculating adomian polynomials for nonlinear operators , 2000, Appl. Math. Comput..

[24]  Y. Cherruault Convergence of Adomian's method , 1990 .

[25]  Dogan Kaya,et al.  Comparing numerical methods for Helmholtz equation model problem , 2004, Appl. Math. Comput..

[26]  A. D. Godefroy Blow up of solutions of a generalized Boussinesq equation , 1998 .

[27]  L. R. Scott,et al.  A Comparison of Solutions of Two Model Equations for Long Waves. , 1983 .

[28]  T. Lewis Solitons in Action , 1979 .

[29]  Turitsyn Blow-up in the Boussinesq equation. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  John M. Ball,et al.  REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS , 1977 .

[31]  Y. Cherruault Convergence of Adomian's method , 1989 .

[32]  George Adomian Solving the mathematical model of neurosciences and medicine , 1995 .

[33]  Michael A. Golberg A note on the decomposition method for operator equations , 1999, Appl. Math. Comput..

[34]  Yves Cherruault,et al.  Adomian's polynomials for nonlinear operators , 1996 .

[35]  Y. Cherruault,et al.  Practical formulae for the calculus of multivariable adomian polynomials , 1995 .

[36]  Z An,et al.  New Ideas for Proving Convergence of Decomposition Methods , 2003 .

[37]  Giuseppe Saccomandi,et al.  New results for convergence of Adomian's method applied to integral equations , 1992 .

[38]  P. Christiansen,et al.  Solitary Waves on Nonlinear Elastic Rods , 1984 .

[39]  D. Kaya Explicit Solutions of Generalized Nonlinear Boussinesq Equations , 2001 .

[40]  Abdul-Majid Wazwaz,et al.  A comparison between Adomian decomposition method and Taylor series method in the series solutions , 1998, Appl. Math. Comput..

[41]  A. Rèpaci,et al.  Nonlinear dynamical systems: On the accuracy of adomian's decomposition method , 1990 .

[42]  K. Lonngren Observations of Solitons on Nonlinear Dispersive Transmission Lines , 1978 .

[43]  G. Adomian Nonlinear Stochastic Operator Equations , 1986 .

[44]  Wenhai Chen,et al.  An algorithm for Adomian decomposition method , 2004, Appl. Math. Comput..