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2 votes

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): ...
ConvexHull's user avatar
  • 1,243
4 votes

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 ...
Maxim Umansky's user avatar
1 vote

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' ...
Manuel Borra's user avatar
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
1 vote

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 ...
Wolfgang Bangerth's user avatar
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

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