Numerical Solutions of the Regularized Long-Wave (RLW) Equation Using New Modification of Laplace-Decomposition Method

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In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by solving two test examples of the problem. To see the accuracy of the method, *L*_{2} and *L*_{∞} error norms are calculated.

References

[1] D. H. Peregrine, “Calculation of the Development of an Undular Bore,” Journal of Fluid Mechanics, Vol. 25, No. 2, 1966, pp. 321-330. doi:10.1017/S0022112066001678

[2] Kh. O. Abdullove, H. Bogalubsky and V. G. Markhankov, “One More Example of Inelastic Soliton Interaction,” Physics Letters A, Vol. 56, No. 6, 1976, pp. 427-428.

[3] J. L. Bona, W. G. Pritchard and L. R. Scott, “Numerical Schemes for a Model of Nonlinear Dispersive Waves,” Journal of Computer Physics, Vol. 60, 1985, pp. 167-196.

[4] P. J. Jain and L. Iskandar, “Numerical Solutions of the Regularized Long Wave Equation,” Computer Methods in Applied Mechanics and Engineering, Vol. 20, No. 2, 1979, pp. 195-201. doi:10.1016/0045-7825(79)90017-3

[5] L. R. T. Gardner, G. A. Gardner and A. Dogan, “A Least Squares Finite Element Scheme for RLW Equation,” Communications in Numerical Methods in Engineering, Vol. 11, No. 1, 1995, pp. 59-68.
doi:10.1002/cnm.1640110109

[6] I. Da□ and M. N. Ozer, “Approximation of the RLW Equation by the Least Square Cubic B-Spline Finite Element Method,” Applied Mathematical Modelling, Vol. 25, No. 3, 2001, pp. 221-231.
doi:10.1016/S0307-904X(00)00030-5

[7] Y. keskin and G. Oturanc, “Numerical Solution of Regularized Long Wave Equation by Reduced Differential Transform Method,” Applied Mathematical Sciences, Vol. 4, No. 25, 2010, pp. 1221-1231.

[8] G. Adomian, “Nonlinear Stochastic Operator Equataions,” Academic Press, San Diego, 1986.

[9] G. Adomian, “Solving Frontier Problem of Physics: The Decomposition Method,” Kluwer Academic Publishers, Boston, 1994.

[10] E. Yusufoglu and A. Bekir, “Application of the Variational Iteration Method to the Regularized Long Wave Equation,” Computer & Mathematics with Applications, Vol. 25, 2003, pp. 321-330.

[11] G. Adomian, “Modified Adomian Polynomials,” Mathematical Computation, Vol. 76, No. 1, 1996, pp. 95-97.
doi:10.1016/0096-3003(95)00186-7

[12] A.-M. Wazwaz and S. M. El-Sayed, “A New Modification of the Adomian Decomposition Method for Linear and Nonlinear Operators,” Applied Mathematics and Computation, Vol. 122, No. 3, 2001, pp. 393-405.
doi:10.1016/S0096-3003(00)00060-6

[13] T. S. El-Danaf, M. A. Ramadan and F. E. I. AbdAlaal, “The Use of Adomian Decomposition Method for Solving the Regularized Long-Wave Equation,” Chaos, Solitons & Fractals, Vol. 26, No. 3, 2005, pp. 747-757.
doi:10.1016/j.chaos.2005.02.012

[14] D. Kaya and S. M. El-Sayed, “An Application of the Decomposition Method for the Generalized KdV and RLW Equations,” Chaos, Solitons & Fractals, Vol. 17, No 5, 2003, pp. 869-877. doi:10.1016/S0960-0779(02)00569-6