Hi, why does the sign function need to be used in the following?(adsbygoogle = window.adsbygoogle || []).push({});

---

The given equation is y_tt = 4 y_xx

0 < x < pi, t>0

where y_tt is the 2nd derivative with respect to t, y_xx is 2nd wrt x

Boundary conditions

y(0,t) = 0 and y(pi,t) = 0

And initial conditions

y_t (x,0) = 0 = g(x)

y(x,0) = sin^2 x = f(x)

---

General solution (d'Alembert's solution):

y(x,t) = 1/2[F(x+at) - F(x-at)] + int[G(s)ds] from x-at to x+at

My teacher wrote that F(x) is the odd periodic extension of f(x), and then wrote

F(x) = sign(sinx)sin^2 x

Why?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solving partial differential equations

**Physics Forums | Science Articles, Homework Help, Discussion**