Timeline for 2 point BVP solver: how to compute errors
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2021 at 11:09 | vote | accept | k.dkhk | ||
| Mar 22, 2021 at 10:46 | answer | added | VoB | timeline score: 1 | |
| Mar 22, 2021 at 10:32 | comment | added | Lutz Lehmann | If that were the case, I would have posted it as an answer. It just shows that your solution is qualitatively correct. And could provide an almost correct initialization for the solver. /// I do not know why the existing answer was deleted, the step-halving or doubling strategy is valid. The only additional point is that one needs to use some function space norm, $L^1$ or $L^2$, to even out the larger errors at the rapid transition in the boundary layer. These would dominate a supremum norm, which makes it less suitable for the error analysis. | |
| Mar 22, 2021 at 10:20 | comment | added | k.dkhk | @LutzLehmann Maybe it is just me who is a bit stupid here, but how I can use this to compute errors and order of convergence? Thanks | |
| Mar 21, 2021 at 20:28 | comment | added | Lutz Lehmann | See math.stackexchange.com/questions/1286926/… for a mathematical treatment of the solution approximation. The jump in the first order approximation $$u(x)=-1+x+a\tanh(a(x-x_0)/(2ϵ))$$ is expected to be where $$(-1+x_0)+a = 0 = (0.5+x_0)-a,$$ so that $a=0.75$ and $x_0=1-a=a-0.5=0.25$. | |
| Mar 21, 2021 at 18:27 | history | asked | k.dkhk | CC BY-SA 4.0 |