局部近似特别解法求解交通流中Burgers方程

Local method of approximate particular solutions for Burgers-type equations in traffic flows

针对现有求解Burgers方程的有网格方法,求解时依赖网格划分质量导致求解失败的问题,提出一种无网格方法——局部近似特别解方法。该方法需要建立一个支持域,利用支持域内的点处的径向基函数近似偏微分方程中一阶、二阶偏微分项,生成局部线性方程组,然后推广到全局形成一个大型稀疏线性方程组,最终直接求解这个线性方程组。实验结果表明:该方法的数值解与解析解吻合的程度很好,从而验证了局部近似特别解方法的有效性。

In the solution of Burgers equation,a meshless method-the local method of approximate particular solution is proposed for the problem of wrong results caused by rel- ying on the quality of the mesh in grid methods. LMAPS method needs to create a support region within a few points at the point of which we can approximate first-order and second-order partial differential term to construct low-order linear equations within the local area.Then the global solutions can be obtained by reformulating local matrix in the global and sparse matrix.Some numerical experiments were carried out and the numerical results were in good agreement with analytical solutions. Therefore, the effectiveness of the new method was verified.