期刊论文详细信息
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 卷:316
High-order ADI finite difference schemes for parabolic equations in the combination technique with application in finance
Article; Proceedings Paper
Hendricks, Christian1  Heuer, Christof1  Ehrhardt, Matthias1  Guenther, Michael1 
[1] Berg Univ Wuppertal, Chair Appl Math & Numer Anal AMNA, Gaussstr 20, D-42119 Wuppertal, Germany
关键词: High-order-scheme;    Sparse grids;    Combination technique;    Alternating direction implicit;    Basket option;   
DOI  :  10.1016/j.cam.2016.08.044
来源: Elsevier
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【 摘 要 】

In this article we combine high-order (HO) finite difference discretisations with alternating direction implicit (ADI) schemes for parabolic partial differential equations with mixed derivatives in a sparse grid setting. In each implicit leg of the ADI schemes, we propose a high-order-compact (HOC) discretisation, such that only tridiagonal systems have to be solved. With the help of HO spatial discretisations and ADI schemes solutions with second order accuracy in time and fourth order accuracy in space can be computed. In order to reduce the number of involved grid points we use the combination technique to construct the so called sparse grid solution. The theoretical findings are illustrated by numerical examples with European basket options. (C) 2016 Elsevier B.V. All rights reserved.

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