University of Sussex
Browse
140974833.pdf (337.07 kB)

High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions

Download (337.07 kB)
journal contribution
posted on 2023-06-08, 22:23 authored by Bertram Duering, Christof Heuer
We present a high-order compact finite difference approach for a rather general class of parabolic partial differential equations with time and space dependent coefficients as well as with mixed second-order derivative terms in n spatial dimensions. Problems of this type arise frequently in computational fluid dynamics and computational finance. We derive general conditions on the coefficients which allow us to obtain a high-order compact scheme which is fourth-order accurate in space and second-order accurate in time. Moreover, we perform a thorough von Neumann stability analysis of the Cauchy problem in two and three spatial dimensions for vanishing mixed derivative terms, and also give partial results for the general case. The results suggest unconditional stability of the scheme. As an application example we consider the pricing of European Power Put Options in the multidimensional Black-Scholes model for two and three underlying assets. Due to the low regularity of typical initial conditions we employ the smoothing operators of Kreiss et al. to ensure high-order convergence of the approximations of the smoothed problem to the true solution.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Numerical Analysis

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

5

Volume

53

Page range

2113-2134

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-09-04

First Open Access (FOA) Date

2015-09-04

First Compliant Deposit (FCD) Date

2015-09-03

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC