11—Numerical Analysis 347
By appropriate choice of∆tand∆x, this will haver≤ 1 , causing a dissipation of the wave. Another scheme is
the Lax-Wendroff method.
u(t+ ∆t,x) =u(t,x)−
c∆t
2∆x
[
u(t,x+ ∆x)−u(t,x−∆x)
]
+
c^2 (∆t)^2
2(∆x)^2
[
u(t,x+ ∆x)− 2 u(t,x) +u(t,x−∆x)
]
. (68)
This keeps one more term in the power series expansion.