Heat Equation

Today, we consider the time dependent model problem

$$\dot u-u''= 0, \quad 0 < x < 1, \quad 0 < t < T,$$ (1)

$$u(0,t) = u'(1,t) = 0,$$ (2)

$$u(x,0) = u_0(x),$$ (3)

where $u = u(x,t)$ is the unknown function that we wish to compute and $u_0(x)$ a given indata function.