7
votes
Accepted
Understanding the diffusion error of numerical schemes
Just figured it out. The solution diffuses BY A FACTOR OF $|G|^n$ after n time steps. So in my example, for the low frequency case, if let's say the original signal was a square wave advecting to the ...
- 111
4
votes
Accepted
How to refine $h$ and $\Delta t$ for convergence tests on evolution PDE
Here are a few solutions that you could explore to determine the orders in space and time.
1) Separate study of time error
You can use a given spatial mesh, and perform multiple simulations with finer ...
- 1,943
3
votes
Understanding the diffusion error of numerical schemes
@FB, Apparently you are now sorted, but I just wanted to point out a source
of confusion you may not yet have considered. Many people call $|G|$ the
amplification factor, which I find much more ...
- 1,154
3
votes
Error propagation through an FFT
This has been derived in G. Betta, C. Liguori, and A. Pietrosanto "Propagation of uncertainty in a discrete Fourier transform algorithm, " Measurement, vol. 27, no. 4, pp. 231-239, Jun. 2000....
- 141
2
votes
numerical schemes for 1D PDE: for smaller grid size there is an increased roundoff error, larger size more truncation, so sweet spot in between?
I think there are two types of error being conflated here. The first is that if you are using an $n$-th order spatial discretization and an $m$-th order temporal discretization then the total error is ...
- 2,926
2
votes
How to estimate the stage error for Runge kutta method
What you're hoping to prove is (in general) not true.
In words, you want to show that for a method of order $p$, each stage of the Runge-Kutta method also approximates the solution (at $t_n + c_i \...
- 16.7k
2
votes
How to estimate the stage error for Runge kutta method
The extension of Taylor expansions to Runge-Kutta methods are the B-series based on single-rooted trees as formalized by Butcher. Such a series has the general form
$$
\Delta y=\Psi(y,h)=\sum_{\tau\in ...
- 6,129
Only top scored, non community-wiki answers of a minimum length are eligible