1.1 Overview of Hyperbolic Partial Differential Equations

The important concepts of convergence, consistency, and stability are presented and shown to be related by the Lax-Richtmyer equivalence theorem. The chapter concludes with a discussion of the Courant-Friedrichs-Lewy condition and related topics.

Overview of Hyperbolic Partial Differential Equations

The One-Way WaveEquation

$$u_t + au_x = 0$$ solution: $$ u(t,x) = u_0 ( x - at) $$