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Asked by pxg882
on 6 Dec 2012

Hi all,

I have a set of equations that needs to be solved over a very large domain (say x > 1000, where x is the integration range).

What is the best way to do this to ensure accurate results using ode45?

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Answer by Jan Simon
on 6 Dec 2012

This is a very general question. Therefore only a general answer is possible.

- Create the function to be integrated correctly, e.g. avoid numerical problems.
- ODE45 and the other intergrators of Matlab require smooth functions. Therefore avoid commands like: IF, RAND, DATE, TIME, ABS, etc.
- Adjust the relative and absolute tolerance
*appropriately*. It is hard science to define this term accurately. - Control the senistivity of the result to variations of the input: Start the integration at
`y`and`y+eps(y)`and compare the effects. If small variations produce large differences, the system is instable and an accurate integration is not possible with the current choice of tolerances.

It is unclear, why "1000" should be very large. If you simulate vehicel dynamics of a car on different terrain and the measurement units are seconds, this is a small period. If you simulate the molecular dynamics in the engine of the same car, 1000 seconds would be hilariously gigantic.

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