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I have equations like this:

wl[n]= w[n] + Δx*v[n]
ϕl[n]= ϕ[n] + Δx*ρ[n] 
ρl[n] = ρ[n] - Δt*fρ(ρ,v,w,n)
vl[n] = v[n] - Δt*fv(ρ,v,w,Δx,n)

Simulating these equations: enter image description here

Can I use ODE solvers to do it in time, then in space. Or, else, is there a Julia package that can help me to get these equations to be unconditionally stable?

BuddhiLW
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1 Answers1

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Do a semi-discretization in space and then call the ODE solver. This is called the method of lines and is one of the most efficient ways to solve a PDE. Examples of this are shown in Solving Partial Differential Equations in Julia (notebook form). There are libraries which will help you do this as well, such as DiffEqOperators.jl.

Chris Rackauckas
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