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**The modified differential transform method for solving MHD boundary-layer equations.**
*(English)*
Zbl 1197.76156

Comput. Phys. Commun. 180, No. 11, 2210-2217 (2009); corrigendum ibid. 212, 285 (2017).

Summary: A new analytical method (DTM-Padé) was developed for solving magnetohydrodynamic boundary-layer equations. It was shown that differential transform method (DTM) solutions are only valid for small values of independent variable. Therefore the DTM is not applicable for solving MHD boundary-layer equations, because in the boundary-layer problem \(y\rightarrow \infty \). Numerical comparisons between the DTM-Padé and numerical methods (by using a fourth-order Runge-Kutta and shooting method) revealed that the new technique is a powerful method for solving MHD boundary-layer equations.

### MSC:

76W05 | Magnetohydrodynamics and electrohydrodynamics |

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\textit{M. M. Rashidi}, Comput. Phys. Commun. 180, No. 11, 2210--2217 (2009; Zbl 1197.76156)

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### References:

[1] | Hayat, T.; Fetecau, C.; Sajid, M., Analytic solution for MHD Transient rotating flow of a second grade fluid in a porous space, Nonlinear Analysis: Real World Applications, 9, 1619-1627 (2008) · Zbl 1154.76391 |

[2] | Hayat, T.; Javedb, T.; Sajid, M., Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface, Physics Letters A, 372, 3264-3273 (2008) · Zbl 1220.76011 |

[3] | Abdelkhalek, M. M., Heat and mass transfer in MHD flow by perturbation technique, Computational Materials Science, 43, 384-391 (2008) |

[4] | Abel, M. S.; Nandeppanavar, M. M., Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink, Communications in Nonlinear Science and Numerical Simulation, 14, 2120-2131 (2009) · Zbl 1221.76211 |

[5] | Ishak, A.; Nazar, R.; Pop, I., MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux, Communications in Nonlinear Science and Numerical Simulation, 14, 109-118 (2009) · Zbl 1221.76224 |

[6] | Prasad, K. V.; Pal, D.; Datti, P. S., MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet, Communications in Nonlinear Science and Numerical Simulation, 14, 2178-2189 (2009) |

[7] | Wang, C. Y., Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Analysis: Real World Applications, 10, 375-380 (2009) · Zbl 1154.76330 |

[8] | Wang, C. Y., Exact solutions of the steady-state Navier-Stokes equations, Annual Review of Fluid Mechanics, 23, 159-177 (1992) |

[10] | Rashidi, M. M.; Dinarvand, S., Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method, Nonlinear Analysis Real World Applications, 10, 4, 2346-2356 (2009) · Zbl 1163.34307 |

[11] | Sajid, M.; Hayat, T.; Asghar, S., Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt, Nonlinear Dynamics, 50, 27-35 (2007) · Zbl 1181.76031 |

[12] | He, J. H., Approximate solution for nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering, 167, 69-73 (1998) · Zbl 0932.65143 |

[13] | Rashidi, M. M.; Ganji, D. D.; Dinarvand, S., Explicit analytical solutions of the generalized Burger and Burger-Fisher equations by homotopy perturbation method, Numerical Methods for Partial Differential Equations, 25, 2, 409-417 (2008) · Zbl 1159.65085 |

[14] | Allan, F. M., Derivation of the Adomian decomposition method using the homotopy analysis method, Applied Mathematics and Computation, 190, 6-14 (2007) · Zbl 1125.65063 |

[15] | He, J. H., A new approach to non-linear partial differential equations, Communications in Nonlinear Science and Numerical Simulation, 2, 4 (1997) |

[16] | Rashidi, M. M.; Shahmohamadi, H., Analytical solution of three-dimensional Navier-Stokes equations for the flow near an infinite rotating disk, Communications in Nonlinear Science and Numerical Simulation, 14, 7, 2999-3006 (2009) · Zbl 1221.76207 |

[17] | Zhou, J. K., Differential Transformation and Its Applications for Electrical Circuits (1986), Huazhong University Press: Huazhong University Press Wuhan, China, (in Chinese) |

[18] | Chen, C. K.; Ho, S. H., Solving partial differential equations by two dimensional differential transform method, Applied Mathematics and Computation, 106, 171-179 (1999) · Zbl 1028.35008 |

[19] | Ayaz, F., Solutions of the systems of differential equations by differential transform method, Applied Mathematics and Computation, 147, 547-567 (2004) · Zbl 1032.35011 |

[20] | Boyd, J., Padé approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain, Computers in Physics, 11, 299-303 (1997) |

[21] | Hayat, T.; Hussain, Q.; Javed, T., The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet, Nonlinear Analysis: Real World Applications, 10, 966-973 (2009) · Zbl 1167.76385 |

[22] | Chaim, T. C., Hydromagnetic flow over a surface stretching with a power-law velocity, International Journal of Engineering Science, 33, 429-435 (1995) · Zbl 0899.76375 |

[23] | Abdel-Halim Hassan, I. H., Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos Solitons and Fractals, 36, 53-65 (2008) · Zbl 1152.65474 |

[24] | Rashidi, M. M.; Erfani, E., New analytical method for solving Burgers’ and nonlinear heat transfer equations and comparison with HAM, Computer Physics Communications, 180, 1539-1544 (2009) |

[25] | Ismail, HNA.; Abde Rabboh, AA., A restrictive Padé approximation for the solution of the generalized Fisher and Burger-Fisher equations, Applied Mathematics and Computation, 154, 203-210 (2004) · Zbl 1050.65077 |

[26] | Wazwaz, A. M., Analytical approximations and Padé approximants for Volterra’s population model, Applied Mathematics and Computation, 100, 13-25 (1999) · Zbl 0953.92026 |

[27] | Baker, G. A.; Graves-Morris, P., Padé Approximants, Encyclopedia of Mathematics and its Application, vol. 13 (1981), Addison-Wesley Publishing Company: Addison-Wesley Publishing Company New York, (Parts I and II) · Zbl 0468.30032 |

[28] | Baker, G. A., Essential of Padé Approximants (1975), Academic Press: Academic Press London |

[29] | Pavlov, K. B., Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a surface, Magnitnaya Gidrodinamika, 4, 146-147 (1975) |

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