In this paper, the nonic (9th order) B-spline functions which have not been used before for the numerical solutions of the partial differential equations by finite element methods are used to solve numerically the Kawahara equation. These approaches involve the collocation and Galerkin finite element methods based on the nonic B-spline functions in space discretization and second order scheme (Crank-Nicolson method) in time discretization. To see the accuracy of the proposed methods three test problems are demonstrated and the obtained numerical results for both of the methods are compared with the exact solution of the Kawahara equation.
GÖRGÜLÜ, MELİS ZORŞAHİN
"Nonic B-spline algorithms for numerical solution of the Kawahara equation,"
Turkish Journal of Mathematics: Vol. 46:
7, Article 21.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/21