# Numerical Wave Propagation

Chapter

## Abstract

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 where and the initial conditions are

$$
c^2 \frac{{\partial ^2 u}}
{{\partial x^2 }} = \frac{{\partial ^2 u}}
{{\partial t^2 }} = for\left\{ \begin{gathered}
0 < x < \ell , \hfill \\
0 < t, \hfill \\
\end{gathered} \right.
$$

(5.1)

*c*is a positive constant. The boundary conditions are$$
u(0,t) = u(\ell ,t) = 0,
$$

(5.2)

$$
u(x,0) = f(x),{\text{ }}u_t (x,0) = g(x).
$$

(5.3)

## Keywords

Wave Equation Wave Packet Group Velocity Truncation Error Explicit Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media, LLC 2007