Banach Contraction Method and Tanhcoth Approach for the Solitary and Exact Solutions of BurgerHuxley and KuramotoSivashinsky Equations

International Journal of Mathematics Trends and Technology (IJMTT)  
© 2021 by IJMTT Journal  
Volume67 Issue4  
Year of Publication : 2021  
Authors : Liberty Ebiwareme 

10.14445/22315373/IJMTTV67I4P506 
MLA Style: Liberty Ebiwareme "Banach Contraction Method and Tanhcoth Approach for the Solitary and Exact Solutions of BurgerHuxley and KuramotoSivashinsky Equations" International Journal of Mathematics Trends and Technology 67.4 (2021):3146.
APA Style: Liberty Ebiwareme(2021). Banach Contraction Method and Tanhcoth Approach for the Solitary and Exact Solutions of BurgerHuxley and KuramotoSivashinsky Equations International Journal of Mathematics Trends and Technology, 3146.
Abstract
In this paper, the Tanhcoth and Banach contraction methods are proposed to solve the BurgersHuxley and KuramotoSivashinsky equations. The equations under study were first transformed into ordinary differential equations using specialized wave transformations as in Tanhcoth where solitary solutions were obtained, whereas the Banach contraction method gives an analytical solution after a finite number of iterations depending on the parameters. The result obtained showed, the methods are easy to implement, computationally less time consuming, accurate, reliable, promising and efficient.
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Keywords : BurgersHuxley, KuramotoSivashinsky, Tanhcoth, Banach contraction method, Convergence of the Methods, Solitary, Kink, solitons