A non-classical ODE problem

Specific Domains Numerics
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1

I have an evolution problem that I cannot cast in a classical form.

\frac{d}{dt} A u = u + F(u,v) \\ G(u) = 0

Where A is a bad matrix to invert, however (A - \Delta t) is ok to invert. When I’m coding this with an implicit scheme, evolving this equation is mostly ok. I would like to put this problem into DifferentialEquations.jl , but its unclear how to do so in this form without inverting A.

2

It seems to be a DAE in (u,v) = X. You find

B \frac{dX}{dt} = [u+F(u,v), G(u)]

with B=diag(A,0).

So yes, it is handled by the package you mention.

3

DifferentialEquations.jl (more specifically OrdinaryDiffEq.jl) supports Mass matrix DAEs. See Differential Algebraic Equations · DifferentialEquations.jl for details.

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