Timeline for Is it normal to expect the error of simulation of a damped harmonic oscillator to decrease as the damping factor decreases?
Current License: CC BY-SA 3.0
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| Nov 30, 2014 at 17:36 | comment | added | Tobias | See the stability region diagrams in staff.science.uu.nl/~frank011/Classes/numwisk/ch10.pdf (RK4 is one of them). The darkness of the gray-plot within the stability region is the magnitude of the error amplification. The darker the color level for your specific eigen-value times step-size product the less the damping of the truncation error of the method. If the product lies outside the stability region the error explodes and the method is not useable. | |
| Nov 27, 2014 at 1:51 | comment | added | David Ketcheson | Sorry, I don't have time for a detailed answer right now. But your intuition is not generally correct (that is, it may be right or wrong, depending on the integrator and the step size chosen). To be brief, your discretization uses a polynomial approximation to the exponential function and the size of the error depends on how well that polynomial approximates the exponential at the eigenvalues of the ODE system. | |
| Nov 25, 2014 at 19:15 | history | edited | Doug Lipinski | CC BY-SA 3.0 |
Fixed latex to use \left( and \right) and \cos or \sin as needed.
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| Nov 25, 2014 at 15:57 | history | tweeted | twitter.com/#!/StackSciComp/status/537273842939731972 | ||
| Nov 25, 2014 at 15:35 | history | edited | Christian Clason | CC BY-SA 3.0 |
edited tags; edited tags
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| Nov 25, 2014 at 11:21 | history | asked | turnip | CC BY-SA 3.0 |