New answers tagged stability
2
votes
Step size constraint in Euler backward
This answer is about illustrating the comments on the structure of the Jacobian, the resulting Lipschitz constant and its consequences on the step size.
There are only two non-zero entries per row
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6
votes
Stability of Euler forward method
The solution of $\frac{du}{dt} = Au$ is $u(t) = \exp(tA)u(0)$, and explicit Euler approximates $\exp(tA)$ using $\lim_{n\to\infty} \left(I+\frac{t}{n}A\right)^n$. Of course in practice you cannot ...
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6
votes
Accepted
Can this finite difference dispersion be eliminated somehow?
It isn't the spike that's causing the dispersion. The scheme you use has a dispersion relationship whereby waves of different frequency travel at different speeds. Every numerical scheme has such a ...
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