# Search results

1. ### Analytical solution for heat equation with simple boundary conditions

I am trying to solve the following heat equation ODE: d^2T/dr^2+1/r*dT/dr=0 (steady state) or dT/dt=d^2T/dr^2+1/r*dT/dr (transient state) The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2. I have searched the analytical solution for this kind of ODEs in polar coordinate...
2. ### Problem with Crank-Nicholson for solving hyperbolic equations

Thank you so much AlephZero, your comments helps a lot on these issues.
3. ### Problem with Crank-Nicholson for solving hyperbolic equations

Thank you AlephZero. Your reply helps me a lot on understanding the problem itself. About Fourier number and Biot number, I heard them before and I definitely gonna check them out. I tried different theta values in Crank-Nicholson method, e.g. U(t+dt)=U(t)+theta*dU It turns out that with bigger...
4. ### Problem with Crank-Nicholson for solving hyperbolic equations

I am a noob so please let me know if here isn't the right place to post this. Recently I am trying to solve hyperbolic equation m*dU/dt=k*d^2U/dx^2+q using Crank-Nicholson and finite element method. The final form of the solution is to compute the increment of the unknown at each time step...