Title
A new stability result for the modified Craig-Sneyd scheme applied to two-dimensional convection-diffusion equations with mixed derivatives.
Abstract
The Modified Craig-Sneyd scheme is an alternating direction implicit(ADI) type scheme that was introduced by In 't Hout and Welfert (2009) 12 in order to numerically solve multidimensional convection-diffusion equations with mixed-derivative terms. It is one of the most prominent ADI schemes currently known for their efficiency in solving above type of problems. This paper deals with a useful stability result for the Modified Craig-Sneyd scheme when applied to two-dimensional convection-diffusion equations with mixed derivative term. The stability of the scheme is analyzed in the von Neumann framework, effectively taking into account the actual size of the mixed derivative term. This study is relevant to an observation of apparent discrepancy in a real world application of the scheme, i.e., in computational finance. The obtained results not only generalize some of the existing stability results, but also clearly justify this surprising observation theoretically.
Year
DOI
Venue
2016
10.1016/j.amc.2016.03.022
Applied Mathematics and Computation
Keywords
Field
DocType
Convection–diffusion equations,Initial-boundary value problems,ADI schemes,Von Neumann stability analysis,Computational finance
Alternating direction implicit method,Convection–diffusion equation,Mathematical optimization,Computational finance,Mathematical analysis,Von Neumann stability analysis,Mathematics,Von Neumann architecture
Journal
Volume
Issue
ISSN
285
C
0096-3003
Citations 
PageRank 
References 
1
0.40
2
Authors
1
Name
Order
Citations
PageRank
Chittaranjan Mishra110.40