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Numerical Solution of the Three-Dimensional Helmholtz Equation |
| Syed Tauseef Mohyud-Din1**, Ahmet Yιldιrιm2 |
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Syed Tauseef Mohyud-Din, Ahmet Yιldιrιm 2010 Chin. Phys. Lett. 27 060201 |
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Abstract We apply the homotopy analysis method to solve the nonhomogeneous multidimensional partial differential equation model problem. The analytic solutions are calculated in terms of convergent series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling “noise” terms whose sum vanishes in the limit. Numerical results clearly reveal the complete reliability and efficiency of the proposed algorithm.
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02.30.Jr
02.30.Mv
02.60.Cb
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Received: 31 December 2009
Published: 25 May 2010
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| PACS: |
02.30.Jr
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(Partial differential equations)
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02.30.Mv
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(Approximations and expansions)
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02.60.Cb
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(Numerical simulation; solution of equations)
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[1] Qin H H and Wei T 2010 Appl. Math. Model. 34 947
[2] Gillman A, Djellouli R and Amara M 2007 J. Comput. Appl. Math. 204 515
[3] Noor M A and Mohyud-Din S T 2007 Arab. J. Math. Math. Sci. 1 13
[4] Adomian G 1995 Solving Frontier Problems of Physics: The Decomposition Method (Boston: Kluwer Academic)
[5] Howard C E and Dianne P O 1998 J. Comput. Phys. 142 163
[6] Howard C E and Dianne P O 1999 Numerische Mathematik 83 231
[7] Evans D J and Ahmad A R 1998 Int. J. Comput. Math. 68 381
[8] Evans D J, Ergüt M and Bulut H 2003 Int. J. Comput. Math. 80 1189
[9] Liao S J 2004 Int. J. Non-Linear Mech. 39 271
[10] Liao S J 1992 PhD Dissertation (Shanghai: Shanghai Jiao Tong University)
[11] Liao S J 1995 Int. J. Non-Linear Mech. 30 371
[12] Liao S J 1997 Int. J. Non-Linear Mech. 32 815
[13] Liao S J 1999 Int. J. Non-Linear Mech. 34 759
[14] Liao S J 2003 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Boca Raton: CRC)
[15] Liao S J 2004 Appl. Math. Comput. 147 499
[16] Liao S J and Campo A 2002 J. Fluid Mech. 453 411
[17] Liao S J 2003 J. Fluid Mech. 488 189
[18] Ayub M, Rasheed A and Hayat T 2003 Int. J. Eng. Sci. 41 2091
[19] Hayat T, Khan M and Asghar S 2004 Acta Mech. 168 213
[20] Hayat T, Khan M and Asghar S 2004 Appl. Math. Comput. 155 417
[21] Abbasbandy S 2007 Int. Comm. Heat Mass Transfer 34 380
[22] Abbasbandy S 2007 Phys. Lett. A 361 478
[23] Abbasbandy S 2008 Chem. Eng. J. 136 144
[24] Bataineh A S, Noorani M S M and Hashim I 2008 Commun. Nonlin. Sci. Numer. Simulat. 13 2060
[25] Xu H, Liao S J and You X C 2009 Commun. Nonlin. Sci. Numer. Simulat. 14 1152
[26] Xu H and Cang J 2008 Phys. Lett. A 372 1250
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