论文标题
迭代弱近似和用于切换扩散的硬界
Iterative weak approximation and hard bounds for switching diffusion
论文作者
论文摘要
我们建立了一个新型的收敛迭代框架，用于弱近似一般开关扩散。所提出方法的关键理论基础是限制最大开关数，以解开和补偿具有弱耦合的偏微分方程的具有挑战性的系统，以收集独立的偏微分方程，以提供多种准确有效的数值方法。使用迭代近似溶液构建解决方案的上和下边界函数。我们为迭代近似解决方案以及上限和下边界函数提供了严格的合并分析。提供了数值结果来检查我们的理论发现和所提出框架的有效性。
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and compensate a challenging system of weakly coupled partial differential equations to a collection of independent partial differential equations, for which a variety of accurate and efficient numerical methods are available. Upper and lower bounding functions for the solutions are constructed using the iterative approximate solutions. We provide a rigorous convergence analysis for the iterative approximate solutions, as well as for the upper and lower bounding functions. Numerical results are provided to examine our theoretical findings and the effectiveness of the proposed framework.
