Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method
DOI:
https://doi.org/10.24297/jam.v12i8.5075Keywords:
Laplace Adomian Decomposition Method, Adomian's Polynomial, Coupled partial differential equation.Abstract
Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components.Downloads
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References
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[11] Mahmoud S. Rawashdeh1 and Shehu Maitama, SOLVING COUPLED SYSTEM OF NONLINEAR PDE’S USING THE NATURAL DECOMPOSITION METHOD. International Journal of Pure and Applied Mathematics, Volume 92 No. 5 2014, 757-776.
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[14] H. O. AL-Humedi et.al, Modified Algorithm to Compute Adomian's Polynomial for Solving Non-Linear Systems of Partial Differential Equations, Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 51, 2505 – 2521.
[15] M. Dehghan, H. Asgar and S. Mohammad, The Solution of Coupled Burger's Equations Using Adomian–Pade technique, Appl. Math. and Comput. 189, (2008) ,No 2, 1034-1047.
[16] S.M. El- Sayed and D. Kaya, On The Numerical Solution of The System of Two-dimensional Burger's Equations by The Decomposition Method, Appl. Math. and Comput. 158, (2004), 101–109.
[2] J. D. Logan, An Introduction to Nonlinear Partial Differential Equations, Wiley, New York, 1994.
[3] A. M. Wazwaz, The decomposition method applied to systems of partial differential equations and to the reaction-diffusion brusselator model, Appl. Math. Comput., 110 (2000), pp. 251-264.
[4] S. A. Khuri, A Laplace Decomposition Algorithm Applied to Class of Nonlinear Differential Equations, Jour- nal of Applied Mathematics, Vol. 1, No. 4, 2001, pp. 141- 155.
[5] H. Hosseinzadeh, H. Jafari and M. Roohani, Application of Laplace Decomposition Method for Solving Klein- Gordon Equation, World Applied Sciences Journal, Vol.8, No. 7, 2010, pp. 809-813.
[6] M. Khan, M. Hussain, H. Jafari and Y.Khan, Application of Laplace Decomposition Method to Solve Nonlinear Coupled Partial Differential Equations, World Applied Sciences Journal, Vol. 9, No. 1, 2010, pp. 13-19.
[7] E. Yusufoglu , Numerical Solution of Duffing Equation by the Laplace Decomposition Algorithm,†Applied Mathematics and Computation, Vol. 177, No.2, 2006, pp. 572-580. doi:10.1016/j.amc.2005.07.072.
[8] D. Kaya and I.E. Inan, Exact and Numerical Traveling Wave Solutions for Nonlinear Coupled Equations Using Symbolic Computation, Appl. Math.and Comput. 151, (2004) 775-787.
[9] H. Jafari and V. Daftardar-Gejji, Solving Linear and Nonlinear Fractional Diffution and Wave Equations by Adomian Decomposition, Applied Mathematics and Computation, Vol. 180, No. 2, 2006, pp. 488-497. doi:10.1016/j.amc.2005.12.031.
[10] F. Abdelwahid, A mathematical Model of Adomian Polynomials, Applied Mathematics and Computation, Vol. 141, No. 2-3, 2003, pp. 447-453. doi:10.1016/S0096-3003(02)00266-7 .
[11] Mahmoud S. Rawashdeh1 and Shehu Maitama, SOLVING COUPLED SYSTEM OF NONLINEAR PDE’S USING THE NATURAL DECOMPOSITION METHOD. International Journal of Pure and Applied Mathematics, Volume 92 No. 5 2014, 757-776.
[12] A.S. Ravi Kanth and K. Aruna, Differential transform method for solving linear and non-linear systems of partial differential equations, Phys. Lett. A., 372, 6896-6898 (2008).
[13] R. Bellman, B. G. Kashef and J. Casti, Differential Quadrature Technique for The Rapid Solution of Nonlinear Partial Differential equations, J. of Comput. Physics, 10, (1972), No.1, 40-52.
[14] H. O. AL-Humedi et.al, Modified Algorithm to Compute Adomian's Polynomial for Solving Non-Linear Systems of Partial Differential Equations, Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 51, 2505 – 2521.
[15] M. Dehghan, H. Asgar and S. Mohammad, The Solution of Coupled Burger's Equations Using Adomian–Pade technique, Appl. Math. and Comput. 189, (2008) ,No 2, 1034-1047.
[16] S.M. El- Sayed and D. Kaya, On The Numerical Solution of The System of Two-dimensional Burger's Equations by The Decomposition Method, Appl. Math. and Comput. 158, (2004), 101–109.
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Published
2016-09-15
How to Cite
M. Bahgat, M. S. (2016). Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method. JOURNAL OF ADVANCES IN MATHEMATICS, 12(8), 6530–6544. https://doi.org/10.24297/jam.v12i8.5075
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