Banach Contraction Method and Tanh-coth Approach for the Solitary and Exact Solutions of Burger-Huxley and Kuramoto-Sivashinsky Equations

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-4
Year of Publication : 2021
Authors : Liberty Ebiwareme


MLA Style: Liberty Ebiwareme "Banach Contraction Method and Tanh-coth Approach for the Solitary and Exact Solutions of Burger-Huxley and Kuramoto-Sivashinsky Equations" International Journal of Mathematics Trends and Technology 67.4 (2021):31-46. 

APA Style: Liberty Ebiwareme(2021). Banach Contraction Method and Tanh-coth Approach for the Solitary and Exact Solutions of Burger-Huxley and Kuramoto-Sivashinsky Equations International Journal of Mathematics Trends and Technology, 31-46.

In this paper, the Tanh-coth and Banach contraction methods are proposed to solve the Burgers-Huxley and Kuramoto-Sivashinsky equations. The equations under study were first transformed into ordinary differential equations using specialized wave transformations as in Tanh-coth 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 : Burgers-Huxley, Kuramoto-Sivashinsky, Tanh-coth, Banach contraction method, Convergence of the Methods, Solitary, Kink, solitons