0
$\begingroup$

I want to solve the following $$\frac{\partial^2 T}{\partial \rho^2}+\frac{1}{\rho}\frac{\partial T}{\partial \rho}=\frac{1}{\alpha^2}\frac{\partial T}{\partial t}$$ with boundary conditions $$T(\rho, 0)=f(\rho) \qquad 0 \leq \rho \leq 1$$ and $$T(1,t)=0$$

Using Mathematica.

I tried

DSolve[D[T[r, t], {r, 2}] + (1/r)*D[T[r, t], r] = (1/a)*D[T[r, t], t], T[r, t], {r, t}]

but it gives me error.

$\endgroup$
2
$\begingroup$

Try this

PDE = D[T[r, t], {r, 2}] + (1/r)*D[T[r, t], r] == (1/a)*D[T[r, t], t];

DSolve[{PDE, T[r, 0] == f[r], T[1, t] == 0}, T[r, t], {r, t}]
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.