New Successive Approximation Methods for Solving Strongly Nonlinear Jaulent-Miodek Equations
DOI:
https://doi.org/10.25271/sjuoz.2021.9.4.869Keywords:
Jaulent-Miodek, Successive Approximation Method, Laplace Transformation, Padé TechniqueAbstract
In this paper, we propose two new techniques for solving system of nonlinear partial differential equations numerically, which we first combine Laplace transformation method into a successive approximation method. Second, we combine Padé [2,2] technique into the first proposed technique. To test the efficiency of our techniques, Jaulent-Miodek system was used, which contains partial differential equations and has strongly nonlinear terms. Experimental results revealed that the first proposed technique gives better results when the interval of t is small in terms of error approximation in tabular and graphical manners. Moreover, the results also demonstrated that the second proposed technique gives better results regardless of the given interval of t in terms of the least square errors.
References
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Mohamed, M. A. & Torky, M. S. (2013). Numerical solution of nonlinear system of partial differential equations by the Laplace decomposition method and the Pade approximation. American Journal of Computational Mathematics, 3(3), 175.
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.
Tracinà, R. & Khalique, C. M. (n.d.). Recent Advances in Symmetry Groups and Conservation Laws for Partial Differential Equations and Applications.
Adam, B. A. A. (2015). A comparative study of successive approximations method and He-Laplace method. Journal of Advances in Mathematics and Computer Science, 129–145.
Fan, E. (2003). Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics. Chaos, Solitons & Fractals, 16(5), 819–839.
Hashem, H. H. G. (2015). On successive approximation method for coupled systems of Chandrasekhar quadratic integral equations. Journal of the Egyptian Mathematical Society, 23(1), 108–112.
Jafari, H. (2014). A comparison between the variational iteration method and the successive approximations method. Applied Mathematics Letters, 32, 1–5.
Jalili, M., Baktash, E. & Ganji, D. D. (2008). Application of He’s homotopy-perturbation method to strongly nonlinear coupled systems. Journal of Physics: Conference Series, 96(1), 12078.
Mahavidyalaya, U. (2012). Laplace substitution method for solving partial differential equations involving mixed partial derivatives. International Journal of Pure and Applied Mathematics, 78(7), 973–979.
Manaa, S. A., Easif, F. H. & Mahmood, B. A. (2013). Successive Approximation Method for Solving Nonlinear Diffusion Equation with Convection Term. IOSR Journal of Engineering, 3, 28–31.
Mohamed, M. A. & Torky, M. S. (2013). Numerical solution of nonlinear system of partial differential equations by the Laplace decomposition method and the Pade approximation. American Journal of Computational Mathematics, 3(3), 175.
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.
Tracinà, R. & Khalique, C. M. (n.d.). Recent Advances in Symmetry Groups and Conservation Laws for Partial Differential Equations and Applications.
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Published
2021-12-30
How to Cite
Sabali, A. J., Manaa, S. A., & Easif, F. H. (2021). New Successive Approximation Methods for Solving Strongly Nonlinear Jaulent-Miodek Equations. Science Journal of University of Zakho, 9(4), 193–197. https://doi.org/10.25271/sjuoz.2021.9.4.869
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Science Journal of University of Zakho
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