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.
 ----

channelflow.org