随机数据下分数阶守恒律方程的多层Monte Carlo有限差分法
Multi-level Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data
摘要：
我们建立了退化分数阶守恒律方程的随机熵解的概念，该方程在初始数据、对流通量和扩散通量中具有随机性。为了量化解的不确定性，我们设计了一种多层蒙特卡罗有限差分法（MLMC-FDM）来近似随机熵解的系综平均。此外，我们分析了MLMC-FDM的收敛速度，并将其与确定性情况下的收敛速度进行了比较。此外，我们制定的误差与工作估计的多水平估计。最后，我们提出了几个数值实验来证明这些计划的效率和验证在这项工作中得到的理论估计。
英文摘要：
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a multi-level Monte Carlo Finite Difference Method (MLMC-FDM) to approximate the ensemble average of the random entropy solutions. Furthermore, we analyze the convergence rates for MLMC-FDM and compare it with the convergence rates for the deterministic case. Additionally, we formulate error vs. work estimates for the multi-level estimator. Finally, we present several numerical experiments to demonstrate the efficiency of these schemes and validate the theoretical estimates obtained in this work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
