论文标题
对流扩散方程的伪漫游轮廓积分方法
Pseudospectral roaming contour integral methods for convection-diffusion equations
论文作者
论文摘要
我们在最近的文献中概括了思想，并开发了新的思想，以便为线性对流扩散PDE，尤其是在金融中出现的一般轮廓积分方法。这些方法旨在通过计算其反拉动段变换来提供解决方案的数值近似。集成轮廓的选择取决于计算方程领先操作员的一些适当加权的伪谱级集。研究了文献中提出的抛物线和双曲线轮廓，并将其与Guglielmi，López-Fernández和Nino最初提出的椭圆轮廓进行了比较。总而言之 （i）在三个不同的集成概况之间进行了比较； （ii）提出了一种新的快速伪漫游方法； （iii）优化时间窗口的选择，相对于固定时间瞬间，可以任意通过无需额外的计算成本近似解决方案； （iv）广泛关注计算方面，它是matlab代码https://github.com/mattiamanucci/contour_integral_methods.git的参考，此处描述的所有算法均已实现。
We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to provide a numerical approximation of the solution by computing its inverse Laplace transform. The choice of the integration contour is determined by the computation of a few suitably weighted pseudo-spectral level sets of the leading operator of the equation. Parabolic and hyperbolic profiles proposed in the literature are investigated and compared to the elliptic contour originally proposed by Guglielmi, López-Fernández and Nino. In summary, the article (i) provides a comparison among three different integration profiles; (ii) proposes a new fast pseudospectral roaming method; (iii) optimizes the selection of time windows on which one may arbitrarily approximate the solution by no extra computational cost with respect to the case of a fixed time instant; (iv) focuses extensively on computational aspects and it is the reference of the MATLAB code https://github.com/MattiaManucci/Contour_Integral_Methods.git, where all algorithms described here are implemented.
