At times I have used Maxima, Matlab, and Mathematica to solve differential equations but to give specific recommendations more input about the use case is needed.
As powerful as possible? In particularly, I’m trying to solve an infinite-horizon optimal control problem with restrictions on what the inputs can be (e.g., not lower than zero), and the resulting equations are quite gnarly. The premium version of Wolfram Alpha couldn’t really deal with them.
Have you used DifferentialEquations.jl? From my reading, it seems to be the most performant solver out there — and I personally love using Julia and its ecosystem. There are some really interesting talks by Chris Rackauckas about what’s possible with DiffEq/SciML packages — ModelingToolkit.jl seems especially exciting for automating the development of scientific simulations.
I’d appreciate it if someone touched on differential equation solvers
What level and type of application do you need?
Wolfram Alpha can do differential equations for example: https://www.wolframalpha.com/input/?i=y%27+%3D+y+%2B+sin+x
At times I have used Maxima, Matlab, and Mathematica to solve differential equations but to give specific recommendations more input about the use case is needed.
As powerful as possible? In particularly, I’m trying to solve an infinite-horizon optimal control problem with restrictions on what the inputs can be (e.g., not lower than zero), and the resulting equations are quite gnarly. The premium version of Wolfram Alpha couldn’t really deal with them.
In that case, you are probably beyond what I can help you with.
Have you used DifferentialEquations.jl? From my reading, it seems to be the most performant solver out there — and I personally love using Julia and its ecosystem. There are some really interesting talks by Chris Rackauckas about what’s possible with DiffEq/SciML packages — ModelingToolkit.jl seems especially exciting for automating the development of scientific simulations.
Ohh, this looks quite nice, thanks.
Did you end up using DifferentialEquations.jl, or did you prefer a different solver?
I ended up solving the equations either analytically (partially with the help of Phil Trammell), https://forum.effectivealtruism.org/posts/FXPaccMDPaEZNyyre/a-model-of-patient-spending-and-movement-building or through simulations https://github.com/NunoSempere/ReverseShooting
https://github.com/NunoSempere/LaborCapitalAndTheOptimalGrowthOfSocialMovements
Thanks for the update and links.
Mathematica is the most powerful solver I’ve come across (it’s basically Wolfram Alpha with additional computational time).