论文标题
数值分析的凝血碎片方程与奇异速率
Numerical analysis for coagulation-fragmentation equations with singular rates
论文作者
论文摘要
本文介绍了用于求解凝血和多个碎片方程的有限体积方案（FVS）的收敛性，该方程具有局部界限的凝结核，但由于碎裂速率而在原点附近奇异性。多亏了Dunford-Pettis和de la vall $ \急性{e} $ e-e-Poussin定理，这使我们能够使用弱$ l^1 $ compactness参数将数值截断的解决方案的收敛到连续模型的弱解决方案。采取适当的稳定条件，以实现结果。此外，当内核在$ w^{1，\ infty} _ {loc} $ space中时，对于统一网格，将证明一阶错误近似。通过尝试几个测试问题来在数值上验证它。
This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks to the Dunford-Pettis and De La Vall$\acute{e}$e-Poussin theorems which allow us to have the convergence of numerically truncated solution towards a weak solution of the continuous model using a weak $L^1$ compactness argument. A suitable stable condition on time step is taken to achieve the result. Furthermore, when kernels are in $W^{1,\infty}_{loc}$ space, first order error approximation is demonstrated for a uniform mesh. It is numerically validated by attempting several test problems.
