广义Rosenau-Burgers方程的一个差分格式

A Finite Difference Scheme for Generalized Rosenau-Burgers Equation

从动力学系统的实际问题出发,对广义Rosenau-Burgers方程的初边值问题进行了数值研究,揭示了复杂离散动态系统理论中非线性波耗散问题.提出了一个新的两层隐式差分格式,对差分解进行了先验估计,得到了差分解的存在唯一性,并给出了该差分格式的收敛性和稳定性的严格理论.数值实验结果表明该方法简单而有效、稳定性良好.该格式具有理论意义和推广价值.

Based on the study of the dynamic systems, the numerical method of the initial- boundary value problem of generalized Rosenau-Burgers equation was discussed and the dissipation problems of nonlinear wave were revealed. A new implicit finite difference scheme of two-level was proposed and the prior estimate of the finite difference solution was obtained. Existence and uniqueness of numerical solutions were derived. It was proved that the finite difference scheme is convergent and stable. Numerical experiments indicated the scheme is efficient and good stability, the proposed scheme has theoretical significance and availability.