[tex](adsbygoogle = window.adsbygoogle || []).push({});

e^{-2 \lambda}(2r \lambda_r -1) + 1 = 8 \pi r^2G_\Phi(r,\mu)

[/tex]

[tex]

e^{-2 \lambda}(2r \mu_r +1) - 1 = 8 \pi r^2H_\Phi(r,\mu)

[/tex]

where

[tex]

G_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL

d\epsilon

[/tex]

[tex]

H_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL

d\epsilon

[/tex]

If you have a system like this and want to solve it numerically for [tex]\lambda [/tex] and [tex] \mu [/tex] how do you deal with the function [tex] \Phi [/tex]. I mean: It can be any function...i have never solved a system like that before.

thank you.

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# Numerical solutions

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