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# Euler
- [x] Apresentar algoritmo
- [x] Discretizar
# Runge Kutta
- [x] Apresentar Algoritmo
- [ ] DiscretizaR
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### Proposal
Update the adaptive step-size algorithm to capture the stability and conditioning improvements demonstrated in [1].
Feedback would be much appreciated on the technical details of the …
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Dear Developers,
I am using Odeint in a project solving the physical N-body system.
I realized that the Runge Kutta stepper provided could work more efficiently.
When I use the stepper named "runge_…
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After 1 time step the system blows up.
Could be:
- Runge Kutta 4 algorithm
- Bad parameters
Need to also sort non-negative solution.
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We should have leapfrog, midpoint, RK4, etc.
https://math.stackexchange.com/questions/721076/help-with-using-the-runge-kutta-4th-order-method-on-a-system-of-2-first-order-od
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In addition to the Runge-Kutta method, it is advised to have support for additional numerical methods. Especially, symplectic integrators such as Leapfrog should be considered as they conserve energy.
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For `u' = A(u,p,t)*u`. In theory this could apply to arbitrary `f`, but we can just show in documentation how to use the Jacobian for this.
From https://arxiv.org/pdf/1207.0069.pdf :
- [x] Lie–…
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# Complete all the things you have written in the readme
- [x] solving linear equations
- [x] Numerical diffrentiation
- [x] Root finding
- [ ] Numerical integration
- [ ] Tropezoidal
…
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Convert the stability functions' object format to rational and floating point format in stability_function.py. Add warning comments in runge_kutta_method.py.
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Euler physics is okay, but perhaps would should consider Runge-Kutta or Verlet.
Of course, we can implement this on a script-by-script basis. For example, some enemies might require more accurate p…