Exercise 13.2.5
From Maxwell’s equations we can find a way to convert the wave equation to a first-order form that uses only first-order derivatives in space:
ut=c2(vy−wx),vt=uywt=−ux, subject to u=0 on the boundary
- Show that a solution satisfies ut=c2(uxx+uyy)
vty=uyywtx=−uxx
Now what?
- Solve with c=2 in the rectange [−3,3]×[−1,1], u(x,y,0)=exp(x−x2)(9−x2)(1−y2), and v=w=0 at t=0. Use m=50 for x and n=25 for y, solve for 0≤t≤6, and make an animation.