±a

Thus, information propagates along the characteristic paths. These preferred information propagation paths should be considered when solving hyperbolic POEs by numerical methods.

11.3 THE FINITE DIFFERENCE METHOD The objective of a finite difference method for solving a partial differential equation (POE) is to transform a calculus problem into an algebra problem by:

1. Discretizing the continuous physical domain into a discrete finite difference grid 2. Approximating the individual exact partial derivatives in the partial differential

equation (POE) by algebraic finite difference approximations (FOAs) 3. Substituting the FOAs into the POE to obtain an algebraic finite difference

equation (FOE) 4. Solving the resulting algebraic FOEs

These steps are discussed in detail in Section 10.3. That section should be reviewed and considered equally relevant to the finite difference solution of hyperbolic POEs.