gibson:teaching:spring-2018:math445:lecture:timestepping
====== Differences ====== This shows you the differences between two versions of the page.
|
gibson:teaching:spring-2018:math445:lecture:timestepping [2018/04/09 09:15] gibson created |
gibson:teaching:spring-2018:math445:lecture:timestepping [2018/04/09 09:16] (current) gibson [Problem 1] |
||
|---|---|---|---|
| Line 82: | Line 82: | ||
| - | Note that the trajectory computed here is not very accurate. The particle shouldexit the box at the same $y$ value it had when it entered. The problem is we chose quite a large time step $\Delta t = 0.4$, and forward-Euler is only 1st-order accurate (error scales as $\Delta t$). In the next problem, we'll reduce the time step to $\Delta t = 0.01$ and get a more accurate solution --though still not as good as the 4th-order accurate ''ode45'' function. | + | Note that the trajectory computed here is not very accurate. The fluid velocity field is symmetric in $x$, so the particle should exit the box at the same $y$ value it had when it entered. The problem is we chose quite a large time step $\Delta t = 0.4$, and forward-Euler is only 1st-order accurate (error scales as $\Delta t$). In the next problem, we'll reduce the time step to $\Delta t = 0.01$ and get a more accurate solution --though still not as good as the 4th-order accurate ''ode45'' function. |
| ---- | ---- | ||
gibson/teaching/spring-2018/math445/lecture/timestepping.1523290533.txt.gz · Last modified: 2018/04/09 09:15 by gibson
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
