New answers tagged

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 ...
Lutz Lehmann's user avatar
  • 5,519
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 ...
lightxbulb's user avatar
  • 1,271
6 votes

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 ...
Wolfgang Bangerth's user avatar

Top 50 recent answers are included