Linear heat transfer equation

• We consider linear diffusion (heat transfer) equation
  

u(x,t) - temperature distribution along rod in time t

D(u) - diffusivity

f(x,t) - heat sources

• Initial condition: u(x,t)=Init(x)
  

• Border condition: u(0,t)=Border0(t) и u(0,t)=Border1(t)
  

• Unknown function is u(x,t).

Consider linear problem:

Constant diffusivity

No heat sources: