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http://dx.doi.org/10.7858/eamj.2017.006

CUBIC B-SPLINE FINITE ELEMENT METHOD FOR THE ROSENAU-BURGERS EQUATION  

Xu, Ge-Xing (Department of Mathematics, Yanbian University)
Li, Chun-Hua (Department of Mathematics, Yanbian University)
Piao, Guang-Ri (Department of Mathematics, Yanbian University)
Publication Information
East Asian mathematical journal / v.33, no.1, 2017 , pp. 53-65 More about this Journal
Abstract
Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.
Keywords
Cubic B-spline; Backward Euler method; Newton method; Crank-Nicolson difference scheme; Rosenau-Burgers equation;
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