gibson:teaching:spring-2012:iam95:hw1
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gibson:teaching:spring-2012:iam95:hw1 [2012/02/29 10:23] gibson |
gibson:teaching:spring-2012:iam95:hw1 [2012/02/29 10:25] (current) gibson [Problem 2] |
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| versus $r$ where $w(x)$ is the asymptotic state of the PDE simulation and $\hat{w}$ is first the | versus $r$ where $w(x)$ is the asymptotic state of the PDE simulation and $\hat{w}$ is first the | ||
| - | the ODE model from (b), second the reduced-order model from (c), and third the reduced-order | + | the ODE model from (b), second the reduced-order model from %%(c)%%, and third the reduced-order |
| equilibrium. Plot these as three lines in log-log plot of error versus $r$. I suggest | equilibrium. Plot these as three lines in log-log plot of error versus $r$. I suggest | ||
| using $r = 1/16, 1/8, 1/4, 1/2,$ and $1$. | using $r = 1/16, 1/8, 1/4, 1/2,$ and $1$. | ||
| - | Note that the ODE systems for (b) and (c) will be stiff, in that the high-order coefficients evolve | + | Note that the ODE systems for (b) and %%(c)%% will be stiff, in that the high-order coefficients evolve |
| very rapidly until the system equilibrates to and moves slowly on the center manifold. You might need to | very rapidly until the system equilibrates to and moves slowly on the center manifold. You might need to | ||
| use a stiff ODE integrator instead of the classic explicit schemes like RK4. | use a stiff ODE integrator instead of the classic explicit schemes like RK4. | ||
gibson/teaching/spring-2012/iam95/hw1.1330539815.txt.gz ยท Last modified: 2012/02/29 10:23 by gibson
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