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SciML / DifferentialEquations.jl

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
https://docs.sciml.ai/DiffEqDocs/stable/
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Boundary Value Differential Algebraic Equations #223

Open c123w opened 6 years ago

c123w commented 6 years ago

Are there currently any algorithms in DifferentialEquations.jl for solving boundary value problem differential algebraic equations (BVP-DAEs)? I've looked around and can't see any.

If there aren't, it might be helpful to add a few at some point. I appreciate this may be difficult though as the only ready made software which springs to mind is COLDAE (Ascher, U & Spiteri, Raymond. (1995). Collocation Software for Boundary Value Differential-Algebraic Equations. SIAM Journal on Scientific Computing. 15. . 10.1137/0915056.), so other algorithms might have to be coded natively.

ChrisRackauckas commented 6 years ago

If you pair a mass matrix ODEProblem with the shooting methods that gives you a BVP-DAE solver. It would require that the problem isn't sensitive to the boundaries though (that's the standard requirement for shooting). It would probably only take a few lines of code to allow DAEProblem and DDEProblems as well.

Other than that, yes we should really make sure we get a good adaptive collocation method which supports DAEs.