DifferentialEquations.jl

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I am trying to use the Lokta-McKendrick equations with the Differential Equations packages. But I am stuck while trying to transform the system of equations into a form suitable for the package.

I am using Lotka–McKendrick system described here and duplicated in the below image:

In the documentation of the differential equations package, I found examples when dx/dt is defined and dy/dt is defined (like here), but not when they are of the form above (dp/dt + dp/da = ...). Could you kindly point me in the right direction?

I am using the DifferentialEquations v6.17.1 and Julia 1.6.1.

That's a Volterra integral equation. The solution will be in NeuralPDE.jl (https://neuralpde.sciml.ai/dev/) and @ashutosh-b-b is working on these solvers right now. We can use this as the example.

How is it going? Can I help in some way?

Hi @ericqu ! Yes its currently in progress, and will be done soon. You can see the PR here. https://github.com/SciML/NeuralPDE.jl/pull/330

Hello, is this still the preferred solver for Volterra integral equations, or is there a way to do it with Integrals.jl?

Yes, NeuralPDE.jl is still our preferred solver for IDEs.