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Strang time-splitting technique via lumped Galerkin method based on cubic B-splines for the Benjamin-Bona-Mahony-Burgers Equation
  • melike karta
melike karta
Agri Ibrahim Cecen Universitesi

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Abstract

In the present manuscript, we are going to research a numerical scheme of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation using the Strang time-splitting technique based on cubic B-spline lumped Galerkin method. In line with our aim, this equation is split into two sub-equations containing the derivative in time direction. Each sub-equations is applied Galerkin finite element method with cubic B-splines and after that the resulting equations are solved with the Strang time-splitting technique. Stability analysis of numerical algorithm is investigated. Five test problems with both exact solution and not is suggested to test the accuracy and reliability of the presented method. The error norms $L_{2}$ and $L_{\infty}$ with three invariants $I_{1},I_{2}$ and $I_{3}$ are computed and compared with existing studies in the literature and the obtained numerical results are displayed in graphics as well as tables. The numerical results obtained with this new approach set light to the solution of nonlinear equations as an effective mathematical tool.