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--- gibson:teaching:spring-2016:math445:lecture:timestepping [2016/04/14 15:31]
gibson [Problem 2]
+++ gibson:teaching:spring-2016:math445:lecture:timestepping [2016/04/14 18:23] (current)
gibson [Problem 4]
@@ Line 81: / Line 81: @@
  {{ :gibson:teaching:spring-2016:math445:lecture:cylinderpath1.png?direct&400 }}
-Note that the computed trajectory is not very accurate, since we chose quite a large time step $\Delta t = 0.4$, and forward-Euler is only 1st-order accurate (error scales as $\Delta t$).
+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.
 ----
@@ Line 170: / Line 172: @@
   x0 = [-2.8; y];                 % set initial position of particle
-  [t, x] = ode45(@v, [0 T], x0);  % compute x(t) at given values of t
+  [t, x] = ode45(@v, [0 T], x0);  % compute x(t) over range 0 <= t <= T
   plot(x(:,1), x(:,2), 'r-');     % plot the path

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