gibson:teaching:spring-2018:math445:lecture:timestepping

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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] |
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- | 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. |

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gibson/teaching/spring-2018/math445/lecture/timestepping.txt ยท Last modified: 2018/04/09 09:16 by gibson