Two Numerical Schemes for the Solution of the Generalized Rosenau Equation with the help of Operator Splitting Techniques

Authors : Melike KARTA

Pages : 14-28

Doi:10.36753/mathenot.1194255

View : 29 | Download : 4

Publication Date : 2023-03-28

Article Type : Research Paper

Abstract :In the present manuscript, numerical solution of generalized Rosenau equation are applied quintic B-spline collocation and cubic B-spline lumped-Galerkin finite element methods insert ignore into journalissuearticles values(FEMs); together with both Strang splitting technique and the Ext4 and Ext6 techniques based on Strang splitting and derived from extrapolation. In the first instance, the problem is divided into two sub-equations as linear $U_t=\\hat{A}insert ignore into journalissuearticles values(U);$ and nonlinear $U_t=\\hat{B}insert ignore into journalissuearticles values(U);$ in the time term. Later, these sub-equations is implemented collocation and lumped-Galerkin insert ignore into journalissuearticles values(FEMs); using quintic and cubic B-spline functions respectively, with Strang insert ignore into journalissuearticles values($S\\Delta t=\\hat{A}-\\hat{B}-\\hat{A}$);, Ext4 and Ext6 splitting techniques. The numerical solutions of the system of ordinary differential equations obtained in this way are solved with help fourth order Runge-Kutta method. The aim of this study is to obtain superior results. For this, a test problem is selected to show the accuracy and efficiency of the method and the error norm results produced by these techniques have been compared among themselves and with the current study in the literature. İt can be clearly stated that it is concluded that the approximate results obtained with the proposed method are better than the study in the literature. So that one can see that the study has achieved its purpose.
Keywords : Generalized Rosenau equation, quintik and cubic B splines, collocation and Galerkin methods, Splitting techniques

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