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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] 2018/04/09 09:16 gibson [Problem 1] 2018/04/09 09:15 gibson created 2018/04/09 09:16 gibson [Problem 1] 2018/04/09 09:15 gibson created 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. ---- ----