[1]
|
A. M. Lyapunov, “The General Problem of the Stability of Motion,” Taylor & Francis, London, 1992
|
[2]
|
J. Saberi-Nadjafi and A. Ghorbani, “He’s Homotopy Perturbation Method: An Effective Tool for Solving Nonlinear Integral and Integro-Differential Equations,” Computers and Mathematics with Applications, Vol. 58, No. 11-12, 2009, pp. 1345-1351.
doi:10.1016/j.camwa.2009.03.032
|
[3]
|
N. H. Sweilam and M. M. Khadar, “Exact Solutions of Some Coupled Nonlinear Partial Differential Equations Using the Homotopy Perturbation Method,” Computers and Mathematics with Applications, Vol. 58, No. 11-12, 2009, pp. 2134-2141. doi:10.1016/j.camwa.2009.03.059
|
[4]
|
A. V. Karmishin, A. I. Zhukov and V. G. Kolosov, “Methods of Dynamic Calculation and Testing for ThinWalled Structure,” Mashinostroyenie, Moscow, 1990.
|
[5]
|
R. Hirota, “Exact Solutions of the Korteweg-deVries Equation for Multiple Collisions of Solitons,” Physics Review Letters, Vol. 27, No. 18, 1971, pp. 1192-1194.
doi:10.1103/PhysRevLett.27.1192
|
[6]
|
A. M. Wazwaz, “On Multiple Soliton Solution for Coupled KdV-mkdV Equation,” Nonlinear Science Letter A, Vol. 1, 2010, pp. 289-296.
|
[7]
|
G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Method,” Kluwer Academic Publication, Boston, 1994.
|
[8]
|
G. C. Wu and J. H. He, “Fractional Calculus of Variations in Fractal Space Time,” Nonlinear Science Letter A, Vol. 1, 2010, pp. 281-287.
doi:10.1515/IJNSNS.2010.11.S1.281
|
[9]
|
M. A. Abdou and A. A. Soliman, “New Application of Variational Iteration Method,” Physica D: Nonlinear Phenomena, Vol. 211, No. 1-2, 2005, pp. 1-8.
doi:10.1016/j.physd.2005.08.002
|
[10]
|
C. Chun, “Fourier-Series Based Variational Iterationmethod for a Reliable Treatment of Heat Equations with Variable Coefficients,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, 2009, pp. 1383-1388. doi:10.1515/IJNSNS.2009.10.11-12.1383
|
[11]
|
N. Faraz, Y. Khan and A. Yildirim, “Analytical Approach to Two-Dimensional Viscous Flow with a Shrinking Sheet via Variational Iteration Algorithm-II,” Journal of King Saud University, Vol. 23, No. 1, 2010, pp. 1-120.
doi:10.1016/j.jksus.2010.06.010.
|
[12]
|
J. H. He, “Variational Iteration Method—A Kind of Nonlinear Analytical Technique: Some Examples,” International Journal of Nonlinear Mechanics, Vol. 34, No. 4, 1999, pp. 699-708.
doi:10.1016/S0020-7462(98)00048-1
|
[13]
|
J. H. He and X. H. Wu, “Variational Iteration Method: New Development and Applications,” Computers and Mathematics with Applications, Vol. 54, 2007, pp. 881-894. doi:10.1016/j.camwa.2006.12.083
|
[14]
|
J. H. He, G. C. Wu and F. Austin, “The Variational Iteration Method Which Should Be Followed,” Nonlinear Science Letter A, Vol. 1, No. 1, 2009, pp. 1-30.
|
[15]
|
E. Hesameddini and H. Latifizadeh, “Reconstruction of Variational Iteration Algorithm Using the Laplace Transform,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, 2009, pp. 1377-1382.
doi:10.1515/IJNSNS.2009.10.11-12.1377
|
[16]
|
L. A. Soltani and A. Shirzadi, “A New Modification of the Variational Iteration Method,” Computers and Mathematics with Applications, Vol. 59, No. 1, 2010, pp. 2528-2535. doi:10.1016/j.camwa.2010.01.012
|
[17]
|
G. C. Wu and E. W. M. Lee, “Fractional Variational Iteration Method, and Its Application,” Physics Letter A, Vol. 374, No. 25, 2010, pp. 2506-2509.
doi:10.1016/j.physleta.2010.04.034
|
[18]
|
G. Adomian, “Solution of Physical Problems by Decomposition,” Computers and Mathematics with Applications, Vol. 2, No. 9-10, 1994, pp. 145-154.
doi:10.1016/0898-1221(94)90132-5
|
[19]
|
D. Bahuguna, A. Ujlayan and D. N. Pandey, “Acomparative Study of Numerical Methods for Solving an IntegroDifferential Equation,” Computers and Mathematics with Applications, Vol. 57, 2009, pp. 1485-1493.
doi:10.1016/j.camwa.2008.10.097
|
[20]
|
M. Dehghan, “Weighted Finite Difference Techniques for the One Dimensional Advection-Diffusion Equation,” Applied Mathematics and Computation, Vol. 147, No. 2, 2004, pp. 307-319. doi:10.1016/S0096-3003(02)00667-7
|
[21]
|
D. D. Ganji and A. Sadighi, “Application of He’s Homotopy Perturbation Method to Nonlinear Coupled Systems of Reaction-Diffusion Equations,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, 2006, pp. 411-418. doi:10.1515/IJNSNS.2006.7.4.411
|
[22]
|
D. D. Ganji, “The Application of He’s Homotopy Perturbation Method to Nonlinear Equation Arising in Heat Transfer,” Physics Letter A, Vol. 335, No. 2, 2006, pp. 337-341. doi:10.1016/j.physleta.2006.02.056
|
[23]
|
H. K. Mishra and A. K. Nagar, “He-Laplace Method for Linear and Nonlinear Partial Differential Equations,” Journal of Applied Mathematics, Vol. 2012, 2012, pp. 1-16. doi:10.1155/2012/180315
|
[24]
|
S. T. Mohyud-Din, M. A. Noor and K. I. Noor, “Travelling Wave Solutions of Seventh-Order Generalized KdV Equation Using He’s Polynomials,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, 2009, pp. 227-233. doi:10.1515/IJNSNS.2009.10.2.227
|
[25]
|
A. M. Wazwaz, “A Comparison between the Variational Iteration Method and Adomian Decomposetion Method,” Journal of Computational and Applied Mathematics, Vol. 207, No. 1, 2007, pp. 129-136.
doi:10.1016/j.cam.2006.07.018
|
[26]
|
E. Yusufoglu, “Numerical Solution of Duffing Equation by the Laplace Decomposition Algorithm,” Applied Mathematics and Computation, Vol. 177, No. 1, 2006, pp. 572-580.
|
[27]
|
J. H. He, “Homotopy Perturbation Method: A New Nonlinear Analytical Technique,” Applied Mathematics and Computation, Vol. 135, No. 1, 2003, pp. 73-79.
doi:10.1016/S0096-3003(01)00312-5
|
[28]
|
J. H. He, “Homotopy, Comparion of Homotopy Perturbation Method and Homotopy Analysis Method,” Applied Mathematics and Computation, Vol. 156, 2004, pp. 527-539. doi:10.1016/j.amc.2003.08.008
|
[29]
|
J. H. He, “Homotopy, the Homotopy Perturbation Method for Nonlinear Oscillators with Discontinueties,” Applied Mathematics and Computation, Vol. 151, 2004, pp. 287-292. doi:10.1016/S0096-3003(03)00341-2
|
[30]
|
J. H. He, “Recent Developments of the Homotopy Perturbation Method,” Topological Methods in Nonlinear Analysis, Vol. 31, 2008, pp. 205-209.
|
[31]
|
J. H. He, “New Interpretation of Homotopy Perturbation Method,” International Journal of Modern Physics, Vol. 20, No. 18, 2006, pp. 2561-2568.
doi:10.1142/S0217979206034819
|
[32]
|
J. H. He, “A Coupling Method of Homotopy Technique and a Perturbation Technique for Nonlinear Problems,” International Journal of Nonlinear Mechanics, Vol. 35, 2000, pp. 37-43. doi:10.1016/S0020-7462(98)00085-7
|
[33]
|
J. H. He, “Variational Iteration Method for Autonomous Ordinary Differential Systems,” Applied Mathematics and Computation, Vol. 114, 2000, pp. 115-123.
doi:10.1016/S0096-3003(99)00104-6
|
[34]
|
J. H. He, “Homotopy Perturbation Technique,” Computer methods in Applied Mechanics and Engineering, Vol. 178, No. 3-4, 1999, pp. 257-262.
doi:10.1016/S0045-7825(99)00018-3
|
[35]
|
J. H. He, “A Simple Perturbation Approach to Blasius Equation,” Applied Mathematics and Computation, Vol. 140, No. 2-3, 2003, pp. 217-222.
doi:10.1016/S0096-3003(02)00189-3
|
[36]
|
J. H. He, “Application of Homotopy Perturbation Method to Nonlinear Wave Equation,” Chaos, Solitons, Fractals, Vol. 26, No. 3, 2005, pp. 295-300.
doi:10.1016/j.chaos.2005.03.006
|
[37]
|
J. H. He, “Homotopy Perturbation Method for Solving Boundary Value Problem,” Physics Letter A, Vol. 350, No. 1-2, 2006, pp. 87-88.
doi:10.1016/j.physleta.2005.10.005
|
[38]
|
E. Hesameddini and H. Latifizadeh, “An Optimal Choice of Initial Solutions in the Homotopy Perturbation Method,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, 2009, pp. 1389-1398.
doi:10.1515/IJNSNS.2009.10.11-12.1389
|
[39]
|
E. Hesameddini and H. Latifizadeh, “A New Vision of the He’s Homotopy Perturbation Method,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, 2009, pp. 1415-1424.
doi:10.1515/IJNSNS.2009.10.11-12.1415
|
[40]
|
M. Rafei and D. D. Ganji, “Explicit Solutions of Helmhotz Equation and Fifth-Order KdV Equation Using Homotopy Perturbation Method,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, 2006, pp. 321-328. doi:10.1515/IJNSNS.2006.7.3.321
|
[41]
|
A. M. Siddiqui, R. Mohmood and Q. K. Ghori, “Thin Film Flow of a Third Grade Fluid on a Moving Belt by He’s Homotopy Perturbation Method,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, No. 1, 2006, pp. 7-14.
doi:10.1515/IJNSNS.2006.7.1.7
|
[42]
|
L. Xu, “He’s Homotopy Perturbation Method for a Boundary Layer Equation in Unbounded Domain,” Computers and Mathematics with Applications, Vol. 54, No. 7-8, 2007, pp. 1067-1070. doi:10.1016/j.camwa.2006.12.052
|
[43]
|
J. Biazar, M. Gholamiporshokuhi and B. Ghanbari, “Extracting a General Iterative Method from an Adomian Decomposition Method and Comparing It to the Variational Iteration Method,” Computers and Mathematics with Applications, Vol. 59, No. 2, 2010, pp. 622-628.
doi:10.1016/j.camwa.2009.11.001
|
[44]
|
S. Islam, Y. Khan, N. Faraz and F. Austin, “Numerical Solution of Logistic Differential Equations by Using the Laplace Decomposition Method,” World Applied Sciences Journal, Vol. 8, 2010, pp. 1100-1105.
|
[45]
|
Y. Khan and F. Austin, “Application of the Laplace Decomposition Method to Nonlinear Homogeneous and Non-Homogeneous Advection Equations,” Zeitschrift fuer Naturforschung, Vol. 65, 2010, pp. 1-5.
|
[46]
|
Y. Khan and Q. B. Wu, “Homotopy Perturbation Transform Method for Nonlinear Equations Using He’s Polynomials,” Computers and Mathematics with Applications, Vol. 61, No. 8, 2011, pp. 1963-1967.
doi:10.1016/j.camwa.2010.08.022
|
[47]
|
Y. Khan, “An Effective Modification of the Lap-Lace Decomposition Method for Nonlinear Equations,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, 2009, pp. 1373-1376.
doi:10.1515/IJNSNS.2009.10.11-12.1373
|
[48]
|
S. A. Khuri, “A Laplace Decomposition Algorithm Applied to a Class of Nonlinear Differential Equations,” Journal of Applied Mathematics, Vol. 1, No. 4, 2001, pp. 141-155. doi:10.1155/S1110757X01000183
|
[49]
|
M. Madani and M. Fathizadeh, “Homotopy Perturbation Algorithm Using Laplace Transformation,” Nonlinear Science Letters A, Vol. 1, 2010, pp. 263-267.
|
[50]
|
A. Ghorbani, “Beyond Adomian’s Polynomials: He’s Polynomials,” Chaos, Solitons, Fractals, Vol. 39, 2009, pp. 1486-1492. doi:10.1016/j.chaos.2007.06.034
|
[51]
|
J. H. He, “Homotopy Perturbation Technique,” Computer Methods in Applied Mechanics and Engineering, Vol. 178, No. 3-4, 1999, pp. 257-262.
doi:10.1016/S0045-7825(99)00018-3
|
[52]
|
S. T. Mohyud-Din and A. Yildirim, “Homotopy Perturb-Bation Method for Advection Problems,” Nonlinear Science Letter A, Vol. 1, No. 3, 2010, pp. 307-312.
|
[53]
|
J. H. He, “A New Approach to Nonlinear Partial Differential Equations,” Communications in Nonlinear Science and Numerical Simulation, Vol. 2, 1997, pp. 230-235.
doi:10.1016/S1007-5704(97)90007-1
|
[54]
|
B. A. Finlayson, “The Method of Weighted Residuals and Variational Principles,” Academic Press, London, 1972.
|
[55]
|
M. Inokuti, et al., “General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics,” In: S. NematNasser, Ed., Variational Method in the Mechanics of Solids Pergamon, 1978, pp. 156-162.
|
[56]
|
G. Adomian, “Stochastic System,” Academic Press, London, 1983.
|
[57]
|
G. L. Liu, “Weighted Residual Decomposition Method in Nonlinear Applied Mathematics,” Proceedings of 6th Congress of Modern Mathematics and Mechanics, Suzhou, 1995, pp. 643-648.
|
[58]
|
G. Adomian, “A Review of the Decomposition Method in Applied Mathematics,” Journal of Mathematical Analysis and Application, Vol. 135, No. 2, 1988, pp. 501-544.
|