Solve equation perturbatively

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SUMMARY

The discussion focuses on solving the equation $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$ perturbatively for the variable ##r##. The resulting expression for ##r## is $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. Participants seek guidance on implementing this perturbative solution using Mathematica, specifically in identifying the small parameter for the perturbation. The discussion emphasizes the need for clarity on the perturbative approach and its application in Mathematica.

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  • Knowledge of Taylor series expansion
  • Basic concepts of differential equations
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This discussion is beneficial for physicists, mathematicians, and students who are interested in applying perturbation theory to solve equations, particularly those using Mathematica for computational solutions.

djymndl07
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I have this expression, $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$. Now I want to solve this equation for ##r## perturbatively. This will give the expression $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. I was reading an article where author did this. How can I do this in mathematica?
 
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Which is your small parameter? It is unclear from your post.
 
djymndl07 said:
How can I do this in mathematica?
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