Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've the following explicit scheme in finite differences (for a one dimensional non uniform diffusion problem), being $k$ the time step, $h$ the space step, $A$ the thermal conductivity at position $i$ and $u_i^n$ the diffused quantity at position $i$ on time $n$:

$$u_i^{n+1} = \frac{k}{h^2}A_{i+1/2}u_{i+1} + \frac{k}{h^2}A_{i-1/2}u_{i+1} + [1 - \frac{k}{h^2}(A_{i+1/2} + A_{i-1/2})]u_i$$

We know that $k/h^2 > 0$ and if we assume that $1 - \frac{k}{h^2}(A_{i+1/2} + A_{i-1/2}) \geq 0$ then we can show that the stability condition is: $$ \frac{k}{h^2} \leq \frac{1}{\max(A_{i+1/2} + A_{i-1/2})}\ \forall i$$

I have a proof for this (I don't want to write it all here unless it is necessary) but I want to check it by asking if somebody has used this (or some similar) condition before.

Thanks in advance,


share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.