ABSTRACT
Chapter 17 formally establishes the stability condition for the leapfrog method as applied to hyperbolic partial differential equations. This stability condition, known as the Courant stability condition, is the key to this chapter. It sets a condition on the Δx and Δt difference sizes that result in a stable scheme. The Courant stability condition was presented in Chapter 3, but here we derive and justify it based on a complete mathematical treatment. One warning is that satisfying Courant stability does not guarantee unconditional stability (which is possible with some implicit schemes applied to parabolic partial differential equations, such as the Crank-Nicholson scheme); rather it is a conditional stability. For hyperbolic partial differential equations modeled with any of the various explicit differencing schemes, at best only conditional stability is possible, and the stability condition is typically of a form similar to the Courant stability condition for the leapfrog method.
