Sumudu-Decomposition Method to Solve Generalized Hirota-Satsuma Coupled Kdv System
DOI:
https://doi.org/10.25271/sjuoz.2022.10.2.879Keywords:
Adomian Decomposition Method, Hirota-Satsuma coupled kdv systems, Sumudu Transform methodAbstract
In this work, we take Adomian Decomposition Method (ADM) and combine it with Sumudu Transform method (STM). This connection between the two methods is called Sumudu-Decomposition Method (SDM), then use it to solve generalized Hirota-Satsuma Coupled kdv (H-SC kdv) systems and also we applied the STM, to find the approximate solutions of system one. Then we compare the approximate solutions of the two way with exact solitary solutions. Clarifying the best way through tables and drawings, then discussing the reason for the changes taking place in the roads and which one is closest to the exact solution.
References
Adomian, G. 1988. “A Review of the Decomposition Method in Applied Mathematics.” Journal of Mathematical Analysis and Applications 135 (2): 501–44. https://doi.org/10.1016/0022-247X(88)90170-9.
Adomian, George. 1994. “Solving Frontier Problems of Physics: The Decomposition Method.” Solving Frontier Problems of Physics: The Decomposition Method. https://doi.org/10.1007/978-94-015-8289-6.
Ahmed, Shams, and Tarig Elzaki. 2015. “Solution of Heat and Wave – Like Equations by Adomian Decomposition Sumudu Transform Method.” British Journal of Mathematics & Computer Science 8 (2): 101–11. https://doi.org/10.9734/bjmcs/2015/9225.
Belgacem, Fethi Bin Muhammad. 2009. “Sumudu Applications to Maxwell’s Equations.” Progress in Electromagnetics Research Symposium 1 (January): 765–70. https://doi.org/10.2529/piers090120050621.
Belgacem, Fethi Bin Muhammad. 2010. “Sumudu Transform Applications to Bessel Functions and Equations.” Applied Mathematical Sciences 4 (73–76): 3665–86.
Belgacem, Fethi Bin Muhammed, and Ahmed Abdullatif Karaballi. 2006. “Sumudu Transform Fundamental Properties Investigations and Applications.” Journal of Applied Mathematics and Stochastic Analysis 2006 (May 2005): 1–23. https://doi.org/10.1155/JAMSA/2006/91083.
Bildik, Necdet, and Sinan Deniz. 2016. “The Use of Sumudu Decomposition Method for Solving Predator-Prey Systems.” Mathematical Sciences Letters 5 (3): 285–89. https://doi.org/10.18576/msl/050310.
Eltayeb, Hassan, and Adem Kiliçman. 2012. “Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations.” Abstract and Applied Analysis 2012. https://doi.org/10.1155/2012/412948.
Eltayeb, Hassan, Adem Klçman, and Said Mesloub. 2014. “Application of Sumudu Decomposition Method to Solve Nonlinear System Volterra Integrodifferential Equations.” Abstract and Applied Analysis 2014 (1). https://doi.org/10.1155/2014/503141.
Lawal, O. W., Loyimi, A.C. and Erinle-Ibrahim, L. M. 2018. “Algorithm for Solving a Generalized Hirota-Satsuma Coupled Kdv Equation Using Homotopy Perturbation Transform Method.” Science World Journal 13 (3): 23–28.
Mehdi Hosseini, Said Mohammad, Syed Tauseef Mohyud-Din, and Husain Ghaneai. 2012. “Variational Iteration Method for Hirota-Satsuma Coupled KDV Equation Using Auxiliary Parameter.” International Journal of Numerical Methods for Heat and Fluid Flow 22 (3): 277–86. https://doi.org/10.1108/09615531211208006.
Raslan, K. R. 2004. “The Decomposition Method for a Hirota-Satsuma Coupled KdV Equation and a Coupled MKdV Equation.” International Journal of Computer Mathematics 81 (12): 1497–1505. https://doi.org/10.1080/0020716042000261405.
Wu, Yongtang, Xianguo Geng, Xingbiao Hu, and Siming Zhu. 1999. “A Generalized Hirota–Satsuma Coupled Korteweg–de Vries Equation and Miura Transformations,” no. May: 259–64.
Yagmurlu, Nuri Murat, Berat Karaagac, and Alaattin Esen. 2019. “A Lumped Galerkin Finite Element Method for the Generalized Hirota-Satsuma Coupled KdV and Coupled MKdV Equations.” Tbilisi Mathematical Journal 12 (3). https://doi.org/10.32513/tbilisi/1569463241.
Adomian, George. 1994. “Solving Frontier Problems of Physics: The Decomposition Method.” Solving Frontier Problems of Physics: The Decomposition Method. https://doi.org/10.1007/978-94-015-8289-6.
Ahmed, Shams, and Tarig Elzaki. 2015. “Solution of Heat and Wave – Like Equations by Adomian Decomposition Sumudu Transform Method.” British Journal of Mathematics & Computer Science 8 (2): 101–11. https://doi.org/10.9734/bjmcs/2015/9225.
Belgacem, Fethi Bin Muhammad. 2009. “Sumudu Applications to Maxwell’s Equations.” Progress in Electromagnetics Research Symposium 1 (January): 765–70. https://doi.org/10.2529/piers090120050621.
Belgacem, Fethi Bin Muhammad. 2010. “Sumudu Transform Applications to Bessel Functions and Equations.” Applied Mathematical Sciences 4 (73–76): 3665–86.
Belgacem, Fethi Bin Muhammed, and Ahmed Abdullatif Karaballi. 2006. “Sumudu Transform Fundamental Properties Investigations and Applications.” Journal of Applied Mathematics and Stochastic Analysis 2006 (May 2005): 1–23. https://doi.org/10.1155/JAMSA/2006/91083.
Bildik, Necdet, and Sinan Deniz. 2016. “The Use of Sumudu Decomposition Method for Solving Predator-Prey Systems.” Mathematical Sciences Letters 5 (3): 285–89. https://doi.org/10.18576/msl/050310.
Eltayeb, Hassan, and Adem Kiliçman. 2012. “Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations.” Abstract and Applied Analysis 2012. https://doi.org/10.1155/2012/412948.
Eltayeb, Hassan, Adem Klçman, and Said Mesloub. 2014. “Application of Sumudu Decomposition Method to Solve Nonlinear System Volterra Integrodifferential Equations.” Abstract and Applied Analysis 2014 (1). https://doi.org/10.1155/2014/503141.
Lawal, O. W., Loyimi, A.C. and Erinle-Ibrahim, L. M. 2018. “Algorithm for Solving a Generalized Hirota-Satsuma Coupled Kdv Equation Using Homotopy Perturbation Transform Method.” Science World Journal 13 (3): 23–28.
Mehdi Hosseini, Said Mohammad, Syed Tauseef Mohyud-Din, and Husain Ghaneai. 2012. “Variational Iteration Method for Hirota-Satsuma Coupled KDV Equation Using Auxiliary Parameter.” International Journal of Numerical Methods for Heat and Fluid Flow 22 (3): 277–86. https://doi.org/10.1108/09615531211208006.
Raslan, K. R. 2004. “The Decomposition Method for a Hirota-Satsuma Coupled KdV Equation and a Coupled MKdV Equation.” International Journal of Computer Mathematics 81 (12): 1497–1505. https://doi.org/10.1080/0020716042000261405.
Wu, Yongtang, Xianguo Geng, Xingbiao Hu, and Siming Zhu. 1999. “A Generalized Hirota–Satsuma Coupled Korteweg–de Vries Equation and Miura Transformations,” no. May: 259–64.
Yagmurlu, Nuri Murat, Berat Karaagac, and Alaattin Esen. 2019. “A Lumped Galerkin Finite Element Method for the Generalized Hirota-Satsuma Coupled KdV and Coupled MKdV Equations.” Tbilisi Mathematical Journal 12 (3). https://doi.org/10.32513/tbilisi/1569463241.
Downloads
Published
2022-04-18
How to Cite
Azzo, S. M., & Manaa, S. A. (2022). Sumudu-Decomposition Method to Solve Generalized Hirota-Satsuma Coupled Kdv System. Science Journal of University of Zakho, 10(2), 43–47. https://doi.org/10.25271/sjuoz.2022.10.2.879
Issue
Section
Science Journal of University of Zakho
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work, with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online.
