ABSTRACT

In this chapter we will introduce finite difference methods used for numerically solving partial differential equations (PDEs). This chapter will focus on the most commonly used finite difference techniques utilized to solve PDEs, namely, explicit, implicit, Crank-Nicolson, and multi-step schemes. We will then apply these methods to solving the heat equation, which is an excellent example that not only illustrates the critical issues we need to consider when applying finite difference methods, but can in fact be related to the Black-Scholes PDE through variable and coordinate substitution.