New answers tagged numerics
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 ...
- 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' ...
- 31
5
votes
enough conditions to check that a matrix doesn't have Cholesky factorization while factorizing it
You are trying to figure out what is known as Modified Cholesky. There are a lot of resources on it, but McSweeney's thesis is a good starting point "Modified Cholesky Decomposition and ...
- 2,411
1
vote
Local truncation error of given implicit 1-step scheme
You insert the exact solution on both sides so that $y'(t_{n+1})=f(t_{n+1},y(t_{n+1}))$ and $y''(t_{n})=f'(t_{n},y(t_{n}))$. Thus
\begin{align}
O(h^{p+1})=g(h)&=-y(t+h)+y(t)+\frac{h}{6}[4y'(t)+2y'(...
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