1
$\begingroup$

What would be the courant condition for the following diffusion equation, $$\frac{\partial f}{\partial t}=A(x)\frac{\partial}{\partial x}\left(D(x)\frac{\partial f}{\partial x}\right).$$ For $$\frac{\partial f}{\partial t}=\frac{\partial}{\partial x}\left(D(x)\frac{\partial f}{\partial x}\right)$$ I know the courant condition which is $$\frac{\delta t D(x)}{\delta x^2}\leq\frac{1}{2}$$ but I am not sure whether the courant condition for the first equation is $$\frac{\delta t A(x)D(x)}{\delta x^2}\leq\frac{1}{2}$$ or not.

$\endgroup$

1 Answer 1

2
$\begingroup$

I think it is correct but it might be important to use the maximum value of the functions $A(x)$ and $D(x)$ in the domain of interest

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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