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Numerical simulation of KdV and mKdv equations with initial conditions by the variational iteration method. (English) Zbl 1142.35572
Summary: A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the modified Korteweg-de Vries (mKdV) equations with initial conditions by a variational approach. The exact and numerical solutions obtained by variational iteration method are compared with those obtained by Adomian decomposition method. The comparison shows that the obtained solutions are in excellent agreement.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
65N99 Numerical methods for partial differential equations, boundary value problems
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[1] He, J.H., Commun nonlinear sci numer simul, 2, 4, 230-235, (1997)
[2] He, J.H., Commun nonlinear sci numer simul, 2, 4, 235-236, (1997)
[3] He, J.H., Int J nonlinear mech, 34, 699-708, (1999)
[4] He, J.H., Appl math comput, 114, 115-123, (2000)
[5] He, J.H., Chaos solitons & fractals, 19, 847-851, (2004)
[6] He, J.H., Appl math comput, 143, 539-541, (2003)
[7] He, J.H., Comput meth appl mech eng, 167, 1-2, 57-68, (1998)
[8] He, J.H., Comput meth appl mech eng, 167, 1-2, 69-73, (1998)
[9] He, J.H.; Wan, Y.Q.; Guo, Q., Int J circ theory appl, 32, 629-632, (2004)
[10] Drãgãnescu, G.E.; Cãpãlnãsan, V., Int J nonlinear sci numer simul, 4, 219-226, (2004)
[11] Marinca, V., Int J nonlinear sci numer simul, 3, 107-110, (2002)
[12] Odibat, Z.M.; Momani, S., Int J nonlinear sci numer simul, 7, 27-36, (2006)
[13] Momani, S.; Abuasad, S., Chaos solitons & fractals, 27, 1119-1123, (2006)
[14] Abulwafa, E.M.; Abdou, M.A.; Mahmoud, A.A., Chaos, solitons & fractals, 29, 313, (2006)
[15] Soliman, A.A., Chaos, solitons & fractals, 29, 294, (2006)
[16] Abdou, M.A.; Soliman, A.A., J comput appl math, 181, 245-251, (2005)
[17] Abdou, M.A.; Soliman, A.A., Physica D, 211, 1-8, (2005)
[18] He, J.H.; Wu, X.H., Chaos, solitons & fractals, 29, 108, (2006)
[19] Momani S, Odibat Z. Chaos, Solitons & Fractals, in press. doi:10.1016/j.chaos.2005.10.068. · Zbl 1378.76084
[20] Yan, Z., Appl math comput, 166, 3, 571-583, (2005)
[21] Yan, Z., Appl math comput, 168, 2, 1065-1078, (2005)
[22] Inokvti, M.; Sekine, H.; Mura, T., General use of the Lagrange multiplier in non-linear mathematical physics, ()
[23] He, J.H., Generalized variational principles in fluids, (2003), Science and Culture Publishing House of China, [in Chinese] · Zbl 1054.76001
[24] He, J.H., Mech res commun, 32, 93-98, (2005)
[25] He, J.H., Comput struct, 81, 2079-2085, (2003)
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