Adomian and Adomian-Padé Technique for Solving Variable Coefficient Variant Boussinesq System
DOI:
https://doi.org/10.25271/sjuoz.2018.6.3.514Keywords:
Adomian, Adomian-Padé, Variable-Coefficient Variant Boussinesq System, Boussinesq-Burgers (B-B)Abstract
In this paper, Adomian and Adomian-Padé Technique are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System, and using Adomian-Padé Technique for Debug (Remove) The Gap (Complex Root).
References
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[6] Wang, Y.-H., "CTE Method to the Interaction Solutions of Boussinesq–Burgers Equations, " Applied Mathematics Letters, Vol. 38, pp. 100-105, (2014).
[7] Gupta, A. K. and Saha Ray, S, "Comparison between Homotopy Perturbation Method and Optimal Homotopy Asymptotic Method for the Soliton Solutions of Boussinesq–Burger Equations," Computers & Fluids, Vol. 103, No., pp. 34-41, (2014).
[8] F. H. Easif, S. A. Manaa, and D. Mekaeel, "Adomain Decomposition Method for∅ 4 Klein Gordon Equation," International Journal of Engineering Inventions, vol. 2, pp. 37-42, (2013).
[9] Abderrahmane AKKOUCHE, Ahmed MAIDI, and M. AIDENE, "Solving Optimal Control Problems by Variational Approach Based on the Adomian’s Decomposition Method," 3rd International Conference on Systems and Control, pp. 218-223, October, (2013).
[10] M. A. Mohamed and M. Torky, "A comparative study of numerical methods for solving the generalized Ito system," Journal of the Egyptian Mathematical Society, vol. 22, pp. 102–114, April (2014).
[11] T. A. Abassy, M. A. EI-Tawil, and H. K. Saleh, "The Solution of KdV and mKdV Equations Using Adomian Pade Approximation," International Journal of Nonlinear Sciences and Numerical Simulation, vol. 5(4), pp. 327-339, (2004).
[12] T. A. Abassy, M. A. El-Tawil, and H. K. Saleh, "The solution of Burgers’ and good Boussinesq equations using ADM–Padé technique," Chaos, Solitons & Fractals, vol. 32, pp. 1008-1026, 5, (2007).
[13] M. A. Mohamed and M. S. Torky, "Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation," American journal of computational mathematics, vol. 3, pp. 175-184, (2013).
[2] Mikhailov, M. D. and Ozisik, M. N, "Unified Analysis and Solutions of Heat and Mass Diffusion, " Dover Publications, (1984).
[3] Swartz, E. T. and Pohl, R. O., "Thermal Resistance at Interfaces, " Applied Physics Letters, Vol. 51, No. 26, pp. 2200-2202, (1987).
[4] Singh, K. and Gupta, R. K., "Exact Solutions of a Variant Boussinesq System, " International Journal of Engineering Science, Vol. 44, No. 18–19, pp. 1256-1268, (2006).
[5] Mei, J. and Ma, Z., "N-Fold Darboux Transformation and Multi-Soliton Solutions for the Classical Boussinesq–Burgers System, " Applied Mathematics and Computation, Vol. 219, No. 11, pp. 6163-6169, (2013),.
[6] Wang, Y.-H., "CTE Method to the Interaction Solutions of Boussinesq–Burgers Equations, " Applied Mathematics Letters, Vol. 38, pp. 100-105, (2014).
[7] Gupta, A. K. and Saha Ray, S, "Comparison between Homotopy Perturbation Method and Optimal Homotopy Asymptotic Method for the Soliton Solutions of Boussinesq–Burger Equations," Computers & Fluids, Vol. 103, No., pp. 34-41, (2014).
[8] F. H. Easif, S. A. Manaa, and D. Mekaeel, "Adomain Decomposition Method for∅ 4 Klein Gordon Equation," International Journal of Engineering Inventions, vol. 2, pp. 37-42, (2013).
[9] Abderrahmane AKKOUCHE, Ahmed MAIDI, and M. AIDENE, "Solving Optimal Control Problems by Variational Approach Based on the Adomian’s Decomposition Method," 3rd International Conference on Systems and Control, pp. 218-223, October, (2013).
[10] M. A. Mohamed and M. Torky, "A comparative study of numerical methods for solving the generalized Ito system," Journal of the Egyptian Mathematical Society, vol. 22, pp. 102–114, April (2014).
[11] T. A. Abassy, M. A. EI-Tawil, and H. K. Saleh, "The Solution of KdV and mKdV Equations Using Adomian Pade Approximation," International Journal of Nonlinear Sciences and Numerical Simulation, vol. 5(4), pp. 327-339, (2004).
[12] T. A. Abassy, M. A. El-Tawil, and H. K. Saleh, "The solution of Burgers’ and good Boussinesq equations using ADM–Padé technique," Chaos, Solitons & Fractals, vol. 32, pp. 1008-1026, 5, (2007).
[13] M. A. Mohamed and M. S. Torky, "Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation," American journal of computational mathematics, vol. 3, pp. 175-184, (2013).
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Published
2018-09-30
How to Cite
Sabali, A. J., Manaa, S. A., & Easif, F. H. (2018). Adomian and Adomian-Padé Technique for Solving Variable Coefficient Variant Boussinesq System. Science Journal of University of Zakho, 6(3), 108–111. https://doi.org/10.25271/sjuoz.2018.6.3.514
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