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This repository has been archived by the owner on Jul 19, 2023. It is now read-only.
Currently the discretization assumes either Dirichlet boundary conditions or 1st order Neumann BCs. There are however PDEs that require higher order BCs; e.g., the beam equation with 3rd order BCs:
@parameters x, t
@variablesu(..)
Dt =Differential(t)
Dtt =Differential(t)^2
Dx =Differential(x)
Dxx =Differential(x)^2
Dx3 =Differential(x)^3
Dx4 =Differential(x)^4
g =-9.81
EI =1
mu =1
L =10.0
dx =0.4
eq =Dtt(u(t,x)) ~-mu*EI*Dx4(u(t,x)) + mu*g
bcs = [u(0, x) ~0,
u(t,0) ~0,
Dx(u(t,0)) ~0,
Dxx(u(t, L)) ~0,
Dx3(u(t, L)) ~0]
# Space and time domains
domains = [t ∈IntervalDomain(0.0,1.0),
x ∈IntervalDomain(0.0,L)]
pdesys =PDESystem(eq,bcs,domains,[t,x],[u(t,x)])
discretization =MOLFiniteDifference([x=>dx],t, centered_order=4)
prob =discretize(pdesys,discretization)
Currently the discretization assumes either Dirichlet boundary conditions or 1st order Neumann BCs. There are however PDEs that require higher order BCs; e.g., the beam equation with 3rd order BCs:
A related issue is also reported here with second order BCs:
https://github.com/SciML/DiffEqOperators.jl/issues/344
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