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Looks awesome. I have a question that might be pedantic but I think you could speak to. Coming from an engineering mindset, I like the use of the term 'integr

Looks awesome. I have a question that might be pedantic but I think you could speak to. Coming from an engineering mindset, I like the use of the term 'integrator' instead of 'solver'. In MATLAB, 'solvers' are used to iterate states of ODE models. But the term 'integrator' is more intuitive to me. Can you speak to the use of one term vs another in the ephemeris community?

constantcrying 3y ago
Solver is a general term, it is just an algorithm which solves a certain problem. You have solvers for linear systems, PDEs, optimization problems, graph problems, etc. An integrator is an algorithm which allows the numerical approximation of the solution to an ODE, given that the ODE is written in a specific form where it is equivalent to calculating the integral of multiple functions.
dreamcompiler 3y ago
You can solve differential equations by integrating or by differentiating. Real-world integrators were easier to build back when DEs were solved with analog computers. Although "easier" is an understatement: Differentiators have a nasty habit of trying to blow up to infinity, which means you can't really build a good, general differentiator either with analog or digital electronics. Integrators are much better behaved pets and they don't shit on the carpet. So everybody uses integrators. Integrators have lots of issues too but those can be sufficiently mitigated for many classes of problems. Differentiators are mostly hopeless, feral beasts.
- mnw21cam 3y ago
  Are you sure you got these the right way round? It seems logical that something that integrates over time should veer off towards infinity eventually, but something that differentiates should be stable.
  - dreamcompiler 3y ago
    Integrals are summers so they can increase without bound over time. But if the input function varies around y=0 -- as many do -- they can remain stable. Now let's talk about infinities that can happen instantly: What's the derivative at the upward edge of a square wave?

constantcrying 3y ago

Solver is a general term, it is just an algorithm which solves a certain problem. You have solvers for linear systems, PDEs, optimization problems, graph problems, etc. An integrator is an algorithm which allows the numerical approximation of the solution to an ODE, given that the ODE is written in a specific form where it is equivalent to calculating the integral of multiple functions.

dreamcompiler 3y ago

You can solve differential equations by integrating or by differentiating. Real-world integrators were easier to build back when DEs were solved with analog computers. Although "easier" is an understatement: Differentiators have a nasty habit of trying to blow up to infinity, which means you can't really build a good, general differentiator either with analog or digital electronics. Integrators are much better behaved pets and they don't shit on the carpet. So everybody uses integrators. Integrators have lots of issues too but those can be sufficiently mitigated for many classes of problems. Differentiators are mostly hopeless, feral beasts.

mnw21cam 3y ago
Are you sure you got these the right way round? It seems logical that something that integrates over time should veer off towards infinity eventually, but something that differentiates should be stable.
- dreamcompiler 3y ago
  Integrals are summers so they can increase without bound over time. But if the input function varies around y=0 -- as many do -- they can remain stable. Now let's talk about infinities that can happen instantly: What's the derivative at the upward edge of a square wave?