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Zbl 1213.65122
Zhou, Shenggao; Cheng, Xiaoliang
A linearly semi-implicit compact scheme for the Burgers-Huxley equation. (English)
[J] Int. J. Comput. Math. 88, No. 4, 795-804 (2011). ISSN 0020-7160; ISSN 1029-0265/e

Summary: A linearly semi-implicit compact scheme is developed for the Burgers-Huxley equation. The equation is decomposed into two subproblems, i.e. a Burgers equation and a nonlinear ordinary differential equation (ODE), by the operator splitting technique. The Burgers equation is solved by a linearly self-starting compact scheme which is fourth-order accurate in space and second-order accurate in time. The nonlinear ODE is discretized by a third-order semi-implicit Runge-Kutta method, which possesses good numerical stability with low computational cost. The numerical experiments show that the scheme provides the expected convergence order. Finally, several experiments are conducted to simulate the solutions of the Burgers-Huxley equation to validate our numerical method.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35Q53 KdV-like equations
65L06 Multistep, Runge-Kutta, and extrapolation methods
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: linearly semi-implicit compact scheme; Burgers-Huxley equation; operator splitting; semi-implicit Runge-Kutta method; stability; numerical experiments; convergence

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Zentralblatt MATH Berlin [Germany]