Numerical Solution of the Burgers' Equation Based on Sinc Method
Subject Areas : Applied MathematicsGhasem Kazemi Gelian 1 , Mohammad Ali Fariborzi Araghi 2
1 - Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran
2 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Keywords:
Abstract :
[1] S. Abbasbandy, M. T. Darvishi, A numerical solution of Burgers'equation
by modied Adomian method, Appl. Math. Comput, 163 (2005)1265-1272.
[2] M. A. Abdou, A. A. Soliman, Variational iteration method for solving
Burgers and coupled Burgers' equations, J. Comput. Appl. Math. 181
(2005) 245-251.
[3] R. Bahadir, M. Saglam, A mixed nite dierence and boundary element
approach to one-dimensional Burgers' equation, Appl. Math. Comput, 160
(2005)663-673.
[4] J. M. Burgers, A mathematical model illustrating the theory of turbulence,
Adv. Appl. Mech, 1 (1948) 171-199.
[5] E. Hopf, The partial dierential equation Ut + UUx = cUxx, Commun.
Pure Appl. Math, 3 (1950) 201-230.
[6] D. Khojasteh Salkuyeh, F. Saadati Sharafeh, On the numerical solution
of the Burgers' equation, International Journal of Computer Mathematics
86 (2009)1334-1344.
[7] S. Kutluaya, A. Esena, I. Dagb, Numerical solutions of the Burgers'
equation by the least-squares quadratic B-spline nite element method,
J. Comput.Appl. Math, 167 (2004) 21-33.
[8] J. Lund, K. Bowers, Sinc Methods for Quadrature and Dierential
Equations, SIAM, Philadelphia, 1992.[9]Z. S. Lu, An explicit Backlund transformation of Burgers' equation with
[9] Z. S. Lu, An explicit Backlund transformation of Burgers' equation with
applications, Commun. Theor. Phys, 44 (2005) 987-989.
[10]V. A. Matveev, M. A. Salle, Darboux Transformation and Solitons,
Springer-Verlag, Berlin, Heidelberg, 1991.
[11] Ozis, E. N. Aksan, A nite element approach for solution of
Burgers'equation, Appl. Math. Comput, 139 (2003) 417-428.
[12]A. A. Soliman, The modied extended tanh-function method for solving
Burgers-type equations, Physica A, 361 (2006) 394-404.
[13] Siraj-ul-Islam, Sirajul Haq, Arshed Ali, Meshfree method for the numerical
solution of the RLW equation, J. Comput. Appl. Math, 223 (2009) 9971012.
[14]F. Stenger, Numerical Methods Based on Sinc and Analytic Functions,
Springer, 1993.
[15] J. W. Thomas, Numerical Partial Dierential Equations: Finite Dierence
Methods, Springer-Verlag, New York, 1995.
[16] A. M. Wazwaz, The tanh and the sine-cosine methods for a reliable
treatment of the modied equal width equation and its variants, Commun,
Nonlinear Sci. Numer. Simul, 11 (2006) 148-160.