Can this equation be modeled by julia

Yes of course:

julia> -1/μ₀ * (∂/∂r) * (∂/r*∂r * (r * Eθ)) - 1/μ₀ ∂^2*Eθ/∂*z^2 + i*ω*σ*Eθ - i*ω*σ * sum(Vₖ/2π*r for i ∈ 1:7) = 0


(more seriously, you will need to provide quite a bit more context to get sensible advice here…)

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This looks like a PDE, you might want to look at GitHub - SciML/MethodOfLines.jl: Automatic Finite Difference PDE solving with Julia SciML. Please post an issue if you get stuck. As a note, you’ll need to seperate your equation in to real and imaginary parts for it to work at the moment.

for more context

sorry it’s in french

what I found it difficult its expressing those integrals in julia

But what do you try to achieve?

i want to vusualise Etheta

Have you heard of quadrature? That is a useful technique for solving integrals. you could construct a quadrature matrix for the integral operators, rearrange and solve.

is it a lybrary on julia?

There is Quadrature.jl, but I’m not sure that this will work for your use case.

What size do you expect the discretized E_theta to be?

10^-3

Is E_theta a function of some parameters, say r, z, t? I mean with what sized array will you approximate it?

E\theta independent to t

if i split the equation to real and imaginari parts does that doesn’t change the solution

The solution is then realpart + im*imagpart

it does’nt work

Read the docs carefully, you will note that that’s not how the differential operators are used. You also need to supply the fact that
E_theta has r, z dependence. Again, consult the docs. There are also a lot of undefined variables used in that equation.

i have to send it by 12 pm
idon know how to visualise it