Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 34

In this chapter we introduce a class of differential equations in which the highest order derivative is one. Furthermore, these equations have a single independent variable (which in nearly all applications plays the role of time). In short, these are termed ordinary differential equations (ODEs) precisely because of the dependence on a single variable.

ODEs crop up in many application areas, such as mechanics, biology, engineering, dynamical systems, economics and finance, to name just a few. It is for this reason that we devote two dedicated chapters to them.

The following topics are discussed in this chapter:

 Motivational examples of ODEs

 Qualitative properties of ODEs

 Common finite difference schemes for initial value problems for ODEs

 Some theoretical foundations.

In Chapter 3 we continue with our discussion of ODEs, including code examples in C++ and Python.