In this paper we aim to compare a popular numerical method with a new, recently proposed meshless approach for Heston PDE resolution. In finance, most famous models can be reformulated as PDEs, which are solved by finite difference and Monte Carlo methods. In particular, we focus on Heston model PDE and we solve it via radial basis functions (RBF) methods and alternating direction implicit. RBFs have become quite popular in engineering as meshless methods: they are less computationally heavy than finite differences and can be applied for high-order problems.

中文翻译：

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关于Heston PDE的数值分辨率的注释

在本文中，我们旨在将一种流行的数值方法与一种新近提出的用于Heston PDE分辨率的无网格方法进行比较。在金融领域，大多数著名的模型都可以重新定义为PDE，可以通过有限差分和蒙特卡洛方法求解。特别是，我们专注于Heston模型PDE，并通过径向基函数（RBF）方法和交替方向隐式求解。RBF作为无网格方法已在工程中变得非常流行：它们的计算量比有限差分少，并且可以应用于高阶问题。