A new algorithm for time dependent Hamilton Jacobi equations on networks, based on semi Lagrangian scheme, is proposed. It is based on the definition of viscosity solution for this kind of problems recently given in. A thorough convergence analysis, not requiring weak semilimits, is provided. In particular, the check of the supersolution property at the vertices is performed through a dynamical technique which seems new. The scheme is efficient, explicit, allows long time steps, and is suitable to be implemented in a parallel algorithm. We present some numerical tests, showing the advantage in terms of computational cost over the one proposed in [7]

翻译：提出了一种基于半拉格朗日格式的网络上时间依赖Hamilton-Jacobi方程的新算法。该算法基于最近对此类问题提出的粘性解定义。我们提供了一种无需弱半极限的全面收敛性分析，特别地，通过一种似乎全新的动态技术验证了顶点处的超解性质。该格式高效、显式、允许长时间步长，并适合并行算法实现。我们给出了一些数值测试结果，展示了在计算成本方面相对于文献[7]中方法的优势。