© Hairem/Shutterstock
CHAPTER 16
Numerical Solutions of Partial Differential Equations
In Section 6.5 we saw that one way of approximating a solution of a second-order boundary-value problem is to work with a finite difference equation replacement of the linear ordinary differential equation. The difference equation is constructed by replacing the ordinary derivatives dy/dx and d2y/dx2 with difference quotients. We will see in this chapter that the same idea carries over to boundary-value problems involving linear partial differential equations.