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Team:Paris/Network analysis and design/Core system/Mathematical analysis and simulations/Integration methods
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* Numerical simulations with Euler algorithm | * Numerical simulations with Euler algorithm | ||
| - | [[Image:simueuler.jpg| | + | [[Image:simueuler.jpg|center]][[Image:simueulerzoom.jpg|center]] |
(The second picture is just a zoom, as defined by the red box) | (The second picture is just a zoom, as defined by the red box) | ||
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* Numerical simulations with variable-step methods | * Numerical simulations with variable-step methods | ||
| - | [[Image:simuode45.jpg| | + | [[Image:simuode45.jpg|center]][[Image:simuode45zoom.jpg|center]] |
(The second picture is just a zoom, as defined by the red box) | (The second picture is just a zoom, as defined by the red box) | ||
One can notice that some oscillations seem to occur in the second case, which is not the case in simulations made with constant step. Therefore, the precise tuning of the algorithm used have to be undertaken in order to avoid false detection of oscillations. | One can notice that some oscillations seem to occur in the second case, which is not the case in simulations made with constant step. Therefore, the precise tuning of the algorithm used have to be undertaken in order to avoid false detection of oscillations. | ||
Revision as of 13:51, 26 October 2008
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Impact of integration methods
Simulations and quick comparison between numerical methodsThis section wil just be made of some simulations to show the influence of the solver used. Indeed, when it comes to detect oscillations, some weird phenomenon can just be produced by simulation algorithms' aterfact. We have just obtained the following curves for the same initial system of ODEs.
  (The second picture is just a zoom, as defined by the red box)
  (The second picture is just a zoom, as defined by the red box) One can notice that some oscillations seem to occur in the second case, which is not the case in simulations made with constant step. Therefore, the precise tuning of the algorithm used have to be undertaken in order to avoid false detection of oscillations. |
