Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 48

In this chapter we gave an introduction to scalar ODEs and systems of ODEs. The main goal was to help the reader become acquainted with their mathematical and numerical foundations as well as become familiar with the associated notation. We recommend learning the main concepts in this chapter because many of them will be used and needed when we model one-factor and two-factor convection-diffusion-reaction PDEs such as the Black–Scholes equation, for example.

Contrary to popular thinking, there is more to ODEs than trying to find analytical solutions for them. Very few ODEs have analytical solutions, and we must resort to ODE solvers.