Numerical Methods For The Burgers-Fisher Equation

In this paper, the numerical methods for the Burgers-Fisher equation of the initial-boundary problem are investigated. Burgers-Fisher equation shows a prototype model for describing convection effects and diffusion transports. Firstly, we propose an implicit difference scheme for Burgers-Fisher equation. On the basis of the priori estimates for numerical solution, the stability analysis is discussed. Numerical experiment results demonstrate that the scheme has error of O (τ+ h~2). Secondly, we propose the Front Time Central Space scheme and leap-frog scheme for Burgers-Fisher equation, using subdomain precise integration method. Numerical experiment results demonstrate that the scheme has high precision. At last, we propose padéapproximation scheme for Burgers-Fisher equation. The stability analysis is discussed. Numerical experiment results demonstrate that the scheme has error of O (τ+ h~2). All those demonstrate that the four schemes are accurate and efficient.