Nugroho's blog.: What About Unbounded End?

## Sunday, May 7, 2017

### What About Unbounded End?

Yeah, what about it? The previous code have the both end bounded.

If we want a free/unbound end, we could set the condition at the with this properties (or we could choose whatever we like)

dy/dx=0

So we will have

y[1]-y[0]=0
y[0] = y[1]

if we want both free ends, we could set the other end as well

y[n] = y[n-1]

So, we just have to modify the original just a bit.

Beware though, with both ends free, we could lost the strings, :)

Here's the code
```from pylab import *
import matplotlib.animation as animation

fig,ax = subplots()

def waves(y0,y1,cb):
y2 = y0
for i in range(1,len(y0)-1):
y2[i] = 2*y1[i]-y0[i]+cb*(y1[i+1]-2*y1[i]+y1[i-1])
y2[0] = y2[1]
#y2[len(y2)-1]=y2[len(y2)-2]
return y2

x   = linspace(0.,1.,20)
dx  = 1./(len(x))
y0  = sin(2*pi*x)
vy0 = 12.

b   = 1./32.  #dt2/dx2
dt  = sqrt(b*dx*dx)
print dt

c   = 1.

cb  = c*b

y1  = y0 + vy0*dt

print y0
print y1

line,   = ax.plot(x,y0)
def animate(i):
global y0,y1,cb
y2  = waves(y0,y1,cb)
y0  = y1
y1  = y2
line.set_ydata(y0)
return line,

#plot (x,y0)

ani =  animation.FuncAnimation(fig, animate, np.arange(1,200), interval =  25, blit=False)

grid(True)
ylim(-10,10)
show()

```
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