- Volume 18 Issue 3
DOI QR Code
INTERNAL FEEDBACK CONTROL OF THE BENJAMIN-BONA-MAHONY-BURGERS EQUATION
- Piao, Guang-Ri (DEPARTMENT OF MATHEMATICS, YANBIAN UNIVERSITY) ;
- Lee, Hyung-Chen (DEPARTMENT OF MATHEMATICS, AJOU UNIVERSITY)
- Received : 2014.02.27
- Accepted : 2014.09.11
- Published : 2014.09.25
A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.
Supported by : National Research Foundation of Korea (NRF)
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