Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations

Journal of Computational and Applied Mathematics - Tập 207 Số 1 - Trang 24-34 - 2007
D.D. Ganji1, Ali Sadighi1
1Mazandaran University, Department of Mechanical Engineering, P. O. Box 484, Babol, Iran

Tóm tắt

Từ khóa


Tài liệu tham khảo

Abdou, 2005, Variational iteration method for solving Burger's and coupled Burger's equations, J. Comput. Appl. Math., 181, 245, 10.1016/j.cam.2004.11.032

Abulwafa, 2006, The solution of nonlinear coagulation problem with mass loss, Chaos, Solitons Fractals, 29, 313, 10.1016/j.chaos.2005.08.044

Aziz, 1984

Bildik, 2006, The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations, Internat. J. Nonlinear Sci. Numer. Simul., 7, 65, 10.1515/IJNSNS.2006.7.1.65

El-Shahed, 2005, Application of He's homotopy perturbation method to volterra's integro-differential equation, Internat. J. Nonlinear Sci. Numer. Simul., 6, 163, 10.1515/IJNSNS.2005.6.2.163

Ganji, 2006, Assessment of homotopy-perturbation and perturbation methods in heat radiation equations, Internat. Comm. Heat Mass Transfer, 33, 391, 10.1016/j.icheatmasstransfer.2005.11.001

He, 1998, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng., 167, 57, 10.1016/S0045-7825(98)00108-X

He, 1998, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Comput. Methods Appl. Mech. Eng., 167, 69, 10.1016/S0045-7825(98)00109-1

He, 1999, Variational iteration method—a kind of non-linear analytical technique: some examples, Internat. J. Non-linear Mech., 34, 699, 10.1016/S0020-7462(98)00048-1

He, 1999, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178, 257, 10.1016/S0045-7825(99)00018-3

He, 2000, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput., 114, 115, 10.1016/S0096-3003(99)00104-6

He, 2000, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Internat. J. Non-linear Mech., 35, 37, 10.1016/S0020-7462(98)00085-7

He, 2003, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput., 135, 73, 10.1016/S0096-3003(01)00312-5

He, 2004, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput., 151, 287, 10.1016/S0096-3003(03)00341-2

He, 2005, Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons Fractals, 26, 695, 10.1016/j.chaos.2005.03.006

He, 2005, Homotopy perturbation method for bifurcation of nonlinear problems, Internat. J. Nonlinear Sci. Numer. Simul., 6, 207, 10.1515/IJNSNS.2005.6.2.207

He, 2006, Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern Phys. B, 20, 1141, 10.1142/S0217979206033796

J.H. He, Non-perturbative methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH, Berlin, 2006.

He, 2006, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons Fractals, 29, 108, 10.1016/j.chaos.2005.10.100

Momani, 2006, Application of He's variational iteration method to Helmholtz equation, Chaos, Solitons Fractals, 27, 1119, 10.1016/j.chaos.2005.04.113

Odibat, 2006, Application of variational iteration method to nonlinear differential equations of fractional order, Internat. J. Nonlinear Sci. Numer. Simul., 7, 27, 10.1515/IJNSNS.2006.7.1.27

Pamuk, 2005, Solution of the porous media equation by Adomian's decomposition method, Phys. Lett. A, 344, 184, 10.1016/j.physleta.2005.06.068

Polyanin, 2004

Siddiqui, 2006, Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. Lett. A, 352, 404, 10.1016/j.physleta.2005.12.033

Siddiqui, 2006, Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method, Internat. J. Nonlinear Sci. Numer. Simul., 7, 7, 10.1515/IJNSNS.2006.7.1.7

Soliman, 2006, A numerical simulation and explicit solutions of KdV-Burgers’ and Lax's seventh-order KdV equations, Chaos, Solitons Fractals, 29, 294, 10.1016/j.chaos.2005.08.054

Siddiqui, 2006, Couette and Poiseuille flows for non-Newtonian fluids, Internat. J. Nonlinear Sci. Numer. Simul., 7, 15, 10.1515/IJNSNS.2006.7.1.15