Initial commitv0.0

1 files changed, 55 insertions, 0 deletions

diff --git a/figs/numerical.fig/simpleq/iteration.jl b/figs/numerical.fig/simpleq/iteration.jl
new file mode 100644
index 0000000..f6f044a
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+++ b/figs/numerical.fig/simpleq/iteration.jl
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+# \hat u_n
+function hatun_iteration(e,order,d,v,maxiter)
+  # gauss legendre weights
+  weights=gausslegendre(order)
+
+  # init V and Eta
+  (V,V0,Eta,Eta0)=init_veta(weights,d,v)
+
+  # init u and rho
+  u=Array{Array{Complex{Float64}}}(undef,maxiter+1)
+  u[1]=zeros(Complex{Float64},order)
+  rho=zeros(Complex{Float64},maxiter+1)
+
+  # iterate
+  for n in 1:maxiter
+    u[n+1]=A(e,weights,Eta)\b(u[n],e,rho[n],V)
+    rho[n+1]=rhon(u[n+1],e,weights,V0,Eta0)
+  end
+
+  return (u,rho)
+end
+
+# A
+function A(e,weights,Eta)
+  N=length(weights[1])
+  out=zeros(Complex{Float64},N,N)
+  for i in 1:N
+    k=(1-weights[1][i])/(1+weights[1][i])
+    out[i,i]=k^2+4*e
+    for j in 1:N
+      y=(weights[1][j]+1)/2
+      out[i,j]+=weights[2][j]*(1-y)*Eta[i][j]/(2*(2*pi)^3*y^3)
+    end
+  end
+  return out
+end
+
+# b
+function b(u,e,rho,V)
+  out=zeros(Complex{Float64},length(V))
+  for i in 1:length(V)
+    out[i]=V[i]+2*e*rho*u[i]^2
+  end
+  return out
+end
+
+# rho_n
+function rhon(u,e,weights,V0,Eta0)
+  S=V0
+  for i in 1:length(weights[1])
+    y=(weights[1][i]+1)/2
+    S+=-weights[2][i]*(1-y)*u[i]*Eta0[i]/(2*(2*pi)^3*y^3)
+  end
+  return 2*e/S
+end