Numerical Wave Propagation

Part of the Texts in Applied Mathematics book series (TAM, volume 52)


In studying phenomena in such diverse areas as electrodynamics, fluid dynamics, and acoustics, it is almost inevitable to come across what is known as the wave equation. This ubiquitous equation is a prototype for many of the waves seen in nature, and it is the subject of this chapter. The specific problem we start with is the wave equation
$$ c^2 \frac{{\partial ^2 u}} {{\partial x^2 }} = \frac{{\partial ^2 u}} {{\partial t^2 }} = for\left\{ \begin{gathered} 0 < x < \ell , \hfill \\ 0 < t, \hfill \\ \end{gathered} \right. $$
where c is a positive constant. The boundary conditions are
$$ u(0,t) = u(\ell ,t) = 0, $$
and the initial conditions are
$$ u(x,0) = f(x),{\text{ }}u_t (x,0) = g(x). $$


Wave Equation Wave Packet Group Velocity Truncation Error Explicit Method 
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© Springer Science+Business Media, LLC 2007

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