Numerical solution of fuzzy Hunter-Saxton equation by using Adomian decomposition and Homotopy analysis methods

Subject Areas : Applied Mathematics

Sh Sadigh behzadi ¹

1 - Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran

Received: 2015-09-21 Accepted : 2015-09-21 Published : 2015-12-01

Keywords:

References:

[1] Allahviranloo. T, Ahmady. N, Ahmady. E (2009). A method for
solving n-th order fuzzy linear dierential equations: Comput. Math.
Appl 86: 730-742.
[2] Abbasbandy. S, Allahviranloo. T (2002). Numerical solutions of
fuzzy dierential equations by taylor method: Comput. Methods
Appl. Math. 2: 113-124.
[3] Abbasbany. S (2008). Homptopy analysis method for generalized
Benjamin-Bona-Mahony equation: Zeitschri fur angewandte
Mathematik und Physik ( ZAMP). 59: 51-62.
[4] Abbasbany. S (2010). Homptopy analysis method for the Kawahara
equation: Nonlinear Analysis: Real Wrorld Applications. 11: 307-
312.
[5] Bressan. A, Constantin. A (2005). Global solutions of the Hunter-
Saxton equation: SIAM J. Math. Anal. 37: 996-1026.
[6] Beals. R, Sattinger. D, Szmigielski. J (2001). Inverse scattering
solutions of the Hunter-Saxton equation: Applicable Analysis. 78
: 255-269.
[7] Behriy.S.H, Hashish.H, E-Kalla.I.L , A.Elsaid (2007). A new
algorithm for the decomposition solution of nonlinear dierential
equations: Appl. Math. Comput. 54: 459-466.
[8] El-KallaI.L (2008). Convergence of the Adomian method applied
to a class of nonlinear integral equations: Appl.Math.Comput. 21:
372-376.
[9] Fariborzi Araghi M.A, Sadigh Behzadi.Sh (2009). Solving nonlinear
Volterra-Fredholm integral dierential equations using the modied
Adomian decomposition method: Comput. Methods in Appl. Math.
9: 1-11.
[10] Fariborzi Araghi.M.A ,
Sadigh Behzadi.Sh (2010). Numerical solution of nonlinear Volterra-
Fredholm integro-dierential equations using Homotopy analysis
method: Journal of Applied Mathematics and Computing, DOI:
10.1080/00207161003770394.

[11] Guan.C (2012). Global weak solutions for a periodic two-
component PERIODIC Hunter-Saxton system: Quarterly of
Applied Mathematics. 2: 285-297.
[12] Hunter.J.K, Saxton.R (1991). Dynamics of director elds: SIAM J.
Appl. Math. 51: 1498-1521.
[13] Li.J, Zhang.K (2011). Global existence of dissipative solutions to
the Hunter-Saxton equation via vanishing viscosity: J. Dierential
Equations. 250: 1427-1447.
[14] Khesin.B, Lenells.J, Misiolek.G (2013). Generalized HunterSaxton
equation and the geometry of the group of circle dieomorphisms:
Math. Ann, DOI 10.1007/s00208-008-0250-3.
[15] Lenells.J (2008). Poisson structure of a modied Hunter-Saxton
equation: J. Phys. A: Math. Theor. 41: 1-9.
[16] Lenells.J (2007). The Hunter-Saxton equation describes the geodesic
ow on a sphere: Journal of Geometry and Physics. 57: 2049-2064.
[17] LiaoS.J (2003). Beyond Perturbation: Introduction to the Homotopy
Analysis Method: Chapman and Hall/CRC Press,Boca Raton.
[18] LiaoS.J (2009). Notes on the homotopy analysis method: some
denitions and theorems: Communication in Nonlinear Science and
Numerical Simulation. 14:983-997.
[19] Nadjakhah.M, Ahangari.F (2013). Symmetry Analysis and
Conservation Laws for the Hunter-Saxton Equation: Commun.
Theor. Phys, doi:10.1088/0253-6102/59/3/16.
[20] PenskoiA. V (2002). Lagrangian time-discretization of the Hunter-
Saxton equation: Physics Letters A. 304: 157-167.
[21] BehzadiSh.S (2010). The convergence of homotopy methods
for nonlinear Klein-Gordon equation: J.Appl.Math.Informatics.
28:1227-1237.
[22] behzadiSh.S , Fariborzi Araghi.M.A (2011).
The use of iterative methods for solving Naveir-Stokes equation:
J.Appl.Math.Informatics. 29: 1-15.

3] BehzadiSh.S, Fariborzi AraghiM.A (2011). Numerical solution
for solving Burger's-Fisher equation by using Iterative Methods:
Mathematical and Computational Applications. 16:443-455.
[24] BehzadiSh.S (2011). Numerical solution of fuzzy Camassa-Holm
equation by using homotopy analysis method: Joournal of Applied
Analysis and Computations. 1:1-9.
[25] BehzadiSh.S (2011). Numerical solution
of Hunter-Saxton equation by using iterative methods: Journal of
Information and Mathematical Sciences. 3: 127-143.
[26] BehzadiSh.S (2011). Solving Schrodinger equation by using modied
variational iteration and homotopy analysis methods: Journal of
Applied Analysis and Computations. 4: 427-437.
[27] Wazwaz.A.M (2001). Construction of solitary wave solution and
rational solutions for the KdV equation by ADM.: Chaos,Solution
and fractals. 12: 2283-2293.
[28] YinZ.Y (2004). On the structure of solutions to the periodic Hunter-
Saxton equation: SIAM J. Math. Anal. 36: 272-283.