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

$$ \begin{equation} u_t + au_x = 0 \end{equation}$$ solution: $$ \begin{equation} u(t,x) = u_0 ( x - at) \end{equation}$$ \((t,x)\) plane에서 \(x-at\)가 상수로 유지되는 라인을 characteristics라고 부른다. \(a\)는 the speed of propagation along the characteristic.

One-way wave eq.의 solution은 형태의 변형 없이 speed \(a\)로 진행하는 wave이다.

식(2)는 미분가능성을 요하지 않는다.