Residual Power Series Method for Solving Klein-Gordon Schrödinger Equation
DOI:
https://doi.org/10.25271/sjuoz.2021.9.2.810Keywords:
Residual Power Series Method, Klein Gordon SchrödingerAbstract
In this work, the Residual Power Series Method(RPSM) is used to find the approximate solutions of Klein Gordon Schrödinger (KGS) Equation. Furthermore, to show the accuracy and the efficiency of the presented method, we compare the obtained approximate solution of Klein Gordon Schrödinger equation by Residual Power Series Method(RPSM) numerically and graphically with the exact solution.
References
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[11] Wang, J., Dai, H., & Hui, Y. (2020). Conservative Fourier spectral scheme for higher order Klein-Gordon-Schrödinger equations. Applied Numerical Mathematics, 156, 446-466. https://doi.org/10.1016/j.apnum.2020.05.015.
[12] Zhang, J., & Kong, L. (2016). New energy-preserving schemes for Klein–Gordon–Schrödinger equations. Applied Mathematical Modelling,40(15-16),6969-6982. https://doi.org/10.1016/j.apm.2016.02.026
[2] Alquran, M. (2014). Analytical solutions of fractional foam drainage equation by residual power series method. Mathematical sciences, 8(4), 153-160.
https://doi.org/10.1007/s40096-015-0141-1
[3] Alquran, M. (2015). Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method. J. Appl. Anal. Comput, 5(4), 589-599. https://doi.org/10.11948/2015046
[4] Arqub, O. A. (2013). Series solution of fuzzy differential equations under strongly generalized differentiability. Journal of Advanced Research in Applied Mathematics, 5(1), 31-52. 10.5373/jaram.1447.051912
[5] El-Ajou, A., Arqub, O. A., & Momani, S. (2015). Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: a new iterative algorithm. Journal of Computational Physics, 293, 81-95.
https://doi.org/10.1016/j.jcp.2014.08.004
[6] İnç, M., Korpinar, Z. S., Al Qurashi, M. M., & Baleanu, D. (2016). A new method for approximate solutions of some nonlinear equations: Residual power series method. Advances in Mechanical Engineering, 8(4), 1687814016644580. https://doi.org/10.1177/1687814016644580
[7] Kumar, S., Kumar, A., & Baleanu, D. (2016). Two analytical methods for time-fractional nonlinear coupled Boussinesq–Burger’s equations arise in propagation of shallow water waves. Nonlinear Dynamics, 85(2), 699-715.
https://doi.org/10.1007/s11071-016-2716-2
[8] Manaa, S. A.,& Mosa, N. M. (2019). Residual Power Series Method for Solving Kaup-Boussinesq System. International Journal of Advanced Trends in Computer Science and Engineering, 8(5), 2089–2095.
https://doi.org/10.30534/ijatcse/2019/36852019
[9] Modanli, M., Abdulazeez, S. T., & Husien, A. M. (2020). A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions. Numerical Methods for Partial Differential Equations. https://doi.org/10.1002/num.22683.
[10] Tang, X. Y., & Ding, W. (2007). The general Klein–Gordon–Schrödinger system: modulational instability and exact solutions. Physica Scripta, 77(1), 015004. https://doi.org/10.1088/0031-8949/77/01/015004
[11] Wang, J., Dai, H., & Hui, Y. (2020). Conservative Fourier spectral scheme for higher order Klein-Gordon-Schrödinger equations. Applied Numerical Mathematics, 156, 446-466. https://doi.org/10.1016/j.apnum.2020.05.015.
[12] Zhang, J., & Kong, L. (2016). New energy-preserving schemes for Klein–Gordon–Schrödinger equations. Applied Mathematical Modelling,40(15-16),6969-6982. https://doi.org/10.1016/j.apm.2016.02.026
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Published
2021-06-30
How to Cite
Manaa, S. A., Easif, F. H., & Murad, J. J. (2021). Residual Power Series Method for Solving Klein-Gordon Schrödinger Equation. Science Journal of University of Zakho, 9(2), 123–127. https://doi.org/10.25271/sjuoz.2021.9.2.810
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