Issue 34: rephrase integral as an ODE

[seabbs]

Description

This PR closes #34.

Under the hypothesis that more work has been put into the ODE solvers vs the integrator and that they may therefore be more stable, I recharacterised the integral as an ODE problem and solved it using the ode_rk45 solver (likely worth exploring other options as well as tolerances). This appears to give a 4-5 times speed up and on the test data has no stability issues (i.e no chains out of 600 failed).

I am very unclear as to exactly why apart from above logic about dev time spent.

As part of testing this I have made the simulated logic significantly harder (a mix of window lengths and observation times).

Checklist

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.62%. Comparing base (c81f6dc) to head (2d62937).
Report is 1 commits behind head on main.

Additional details and impacted files

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  Coverage   99.62%   99.62%           
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  Files           7        7           
  Lines         268      268           
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  Hits          267      267           
  Misses          1        1           

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[seabbs]

LGTM (self-review)