作者:王希，张爽，胡劲松
Authors:WANG Xi,ZHANG Shuang,HU Jin-song摘要:摘要:BBM-KdV方程因能描述大量的物理现象如浅水波和离子波等而占有重要的地位，是弱非线性色散介质中长波单向传播的重要模型，其数值研究少有涉及。针对一类带有齐次边界条件的广义BBMKdV方程的初边值问题，提出了一个具有二阶理论精度的两层非线性有限差分格式，合理模拟了问题本身的两个守恒量，并给出差分格式的先验估计，讨论其差分解的存在唯一性，并用离散泛函分析方法证明该格式的收敛性和无条件稳定性，最后通过数值模拟验证了该数值方法的可靠性。
Abstract:Abstract:The BBM-KdV equation plays an important role because it can describe a large number of physical phenomena, such as shallow water waves and ion waves. It is an important model for long-wave unidirectional propagation in weakly nonlinear dispersive media, but its numerical investigations are rarely made. For the initial-boundary value problem of the generalized BBM-KdV equations with homogeneous boundary conditions, a two-level nonlinear finite difference scheme with the second-order theoretical accuracy is proposed, which reasonably simulates the two conserved quantities of the problem. With a priori estimation, the existence and uniqueness of the difference solutions are dicussed. By the discrete functional analysis method the convergence and unconditional stability of the scheme are also proved. Finally, some numerical experiments verify the robustness of the proposed scheme.
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求解广义BBM-KdV方程的守恒型有限差分方法
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