Abstract
The finite difference method, which is the main tool of this book, is used to solve various partial differential equations that arise in mathematical finance. For those who are not experts in this area of numerical analysis but nevertheless want to learn about it, below we give a brief introduction to the subject. Although several dozen useful textbooks about finite differences are available (and some of them we will quote below), it makes sense to provide some basic definitions and notions, so the reader can find at least the basics right here in this book.
The world is continuous, but the mind is discrete.
David Mumford (ICM 2002 plenary talk, August 21, 2002).
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- 1.
Nonuniform grids are considered in the next chapter.
- 2.
In the next section we will give some examples of multilayer schemes, e.g., so-called BDF2 schemes [7].
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Itkin, A. (2017). Basics of the Finite Difference Method. In: Pricing Derivatives Under Lévy Models . Pseudo-Differential Operators, vol 12. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-6792-6_1
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