New answers tagged finite-difference
2
votes
Accepted
Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?
The answer is quite simple:
You have to set the Neumann boundary condition $u_x(-1,x)=0$ explicitly
Add following line (fifth line):
...
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4
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Finite difference problem
Since this is apparently a homework problem, let's just illustrate the idea on a simple small example. Let's take the domain [0,1], with the discontinuity at $x=0.5$, and assume $\alpha$=1 to the left ...
- 2,440
1
vote
Accepted
Does anyone know how to add a forcing term at the center of a cicular membrane?
Once again, my mates and I have successfully deciphered how to tackle this. It's worth noting that when introducing the forcing term, altering 'i' impacts the radial position, while adjusting 'j' ...
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6
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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 ...
- 1,271
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derivative matrix and the Dirac delta distribution
You could, but why would you? We have systematic ways of obtaining finite difference stencils approximating derivatives that do not rely on the derivatives of functions that are zero everywhere and ...
- 54.2k
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 ...
- 54.2k
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