Numerical treatment of Kuramoto-Sivashinsky equation on B-spline collocation
Saumya Ranjan Jena, Guesh Simretab Gebremedhin
Abstract
In this article, a nonic B-spline collocation approach is applied to solve the approximate solution of Kuramoto-Sivashinsky equation (KSE). Here the nonlinear term of KSE is linearizing using Taylor series technique. The main objective of this study is to provide a new class of approach by applying some possible higher-order derivatives rather than lower order derivatives of the nonic B-spline on the boundary conditions of KSE in finding the additional constraints, which help us to obtain a unique solution of the problem. The stability analysis is investigated using the Von-Neumann scheme and the proposed scheme is found to be unconditionally stable. The efficiency and accuracy of the proposed approach are demonstrated by two numerical tests and the current results are compared with the exact solution and result of others in the literature.