Timeline for Numerically inverting an integral
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2017 at 17:36 | comment | added | Robert Israel | Or just compute $\int_0^{t_0} H(s)\; ds = x_0$ for some given $t_0$ and use initial condition $T(x_0) = t_0$. | |
| Aug 11, 2017 at 15:18 | comment | added | Ian | @Alice Proceeding directly, that creates a problem for you indeed. But you can estimate $T(x)$ for small $x$ using some other method (for example, Newton's method, starting from a nonzero initial condition) and then use Robert Israel's suggestion for larger $x$, using that other estimate as your initial condition. | |
| Aug 11, 2017 at 10:51 | comment | added | Alice | For this differential equation, you would have $T(0)=0$ as the initial condition. The problem I then have is that I am actually looking at functions $H$ such that $H(0)=0$. Would this be a problem when trying to solve this ODE since $\frac{dT}{dx}$ is not defined at the IC? (I realise this info should really have been in the initial question, I'll edit it now.) | |
| Aug 11, 2017 at 7:01 | comment | added | Dirk | Nice idea! @Alice, could you comment on how that worked for your problem? | |
| Aug 10, 2017 at 20:44 | history | answered | Robert Israel | CC BY-SA 3.0 |