I am having trouble with finding a solution which satisfies the boundary and initial conditions to this PDE:
∂u∂t=∂2u∂2x\frac{\partial u}{\partial t} = \frac{\partial ^2 u}{\partial^2x}∂t∂u=∂2x∂2u where u=u(x,t)u=u(x,t)u=u(x,t), 0≤x≤L0 \leq x \leq L0≤x≤L with boundary & initial conditions:
BC1: u(x=0,t>0)=Tfu(x=0,t>0)=T_fu(x=0,t>0)=Tf; BC2: u(x=L,t>0)=Tiu(x=L,t>0)=T_iu(x=L,t>0)=Ti; IC: u(x,t=0)=f(x)u(x,t=0)=f(x)u(x,t=0)=f(x)