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The only independent variabls is z, the aim is to solve $\nu$[z], qr[z] and qi[z] from z=0 to z. The parameters are: A[z], B[z], D[z], d[z], and ne[$\rho$,z], $\gamma$[$\rho$,z], $\epsilon$r[$\rho$,z] and $\epsilon$i[$\rho$,z]. The integration of $\rho$ ranges from d to infinite.

The only independent variables is z, the aim is to solve $\nu$[z], qr[z] and qi[z] from z=0 to z. The parameters are: A[z], B[z], D[z], d[z], and ne[$\rho$,z], $\gamma$[$\rho$,z], $\epsilon$r[$\rho$,z] and $\epsilon$i[$\rho$,z]. The integration of $\rho$ ranges from d to infinite.

Do I have to use Runge-Kutta method?

Equations:

I wrote the code with error messages: NDSolve::ndnum: Encountered non-numerical value for a derivative at z == 0.1.

From equations to code, different names are used: $\rho$ -->r, D-->D0, d-->dmin. $\gamma$ -->$\gamma_0$

ClearAll[ν, qr, qi, r, γ, ne, ϵr, ϵi, dmin, A, B, D0, aL, Zni, νei]; aL = 10; Zni = 0.001; νei = 0.001; γ= (1 + aL^2*ν^2*Exp[-2*qr*r^2])^0.5; ne= Zni - 4*qr*γ*(1 -γ^(-2))*(1 - qr*r^2*(1 + γ^(-2))); ϵr= 1 - ne/γ; ϵi= 4*Pi*νei*ne; dmin= Re[qr^(-0.5)*(-0.5*Log[Zni/(8*aL^2*ν^2*qr) (1+sqrt[4+(Zni/(4*qr))^2])])^0.5]; D0[ne_?NumericQ, qr_?NumericQ] := NIntegrate[16*Pi*νei*ne*Exp[-2*qr*r^2]*qr*r, {r, dmin, Infinity}]; A[ν_?NumericQ, qr_?NumericQ, ϵr_?NumericQ, qi_?NumericQ,ϵi_?NumericQ, dmin_?NumericQ] := ν*NIntegrate[r*Exp[-qr*r^2]*((1-ϵr)*Sin[qi*r^2]-ϵi*Cos[qi*r^2]), {r, dmin, Infinity}]; B[ν_?NumericQ, qr_?NumericQ, ϵr_?NumericQ, qi_?NumericQ,ϵi_?NumericQ, dmin_?NumericQ] := ν*NIntegrate[r*Exp[-qr*r^2]*((1-ϵr)*Cos[qi*r^2]+ϵi*Sin[qi*r^2]), {r, dmin, Infinity}]; s = NDSolve[{ ν'[z] == -A[ν[z], qr[z], ϵr,qi[z], ϵi, dmin]*qr[z] - D0[ne, qr[z]]*ν[z], qr'[z] == -2 A[ν[z], qr[z], ϵr,qi[z], ϵi, dmin]*qr[z]^2/ν[z]-D0[ne,qr[z]]*qr[z], qi'[z] == -3 A[ν[z], qr[z], ϵr,qi[z], ϵi, dmin]*qr[z]*qi[z]/ν[z] + B[ν[z], qr[z], ϵr,qi[z], ϵi, dmin]*qr[z]^2/ν[z] - D0[ne, qr[z]]*qi[z], ν[0.1] == 1., qr[0.1] == 10^(-4), qi[0.1] == 0.}, {ν, qr, qi}, {z, 0.1, 10000.}]