(adsbygoogle = window.adsbygoogle || []).push({}); second ODE, initial conditions are zeros at infinity!!

I want to know the temperature profile of phase transition layer in the interstellar medium.

For stationary solution, the dimensionless differential equation I ended up with is

[tex]\frac{d^2T}{dx^2} = \frac{f(T)}{T^2} - \frac{1}{T} [/tex]

where [itex]f(T)[/itex] is some complicated but well-behaved function.

Boundary conditions are

[tex]T(x=-\infty) = 1 ,[/tex]

[tex]\frac{dT}{dx}(x=-\infty) = 0,[/tex]

However, [itex]f(T=1) = 1[/itex], one obtains [itex]\frac{d^2T}{dx^2}(x=-\infty) = 0[/itex]

How do I solve this numerically? where should I start the integration? and what should be the initial condition?

Do I need to Taylor expand the differential equation?

Thank you for your attention.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Second ODE, initial conditions are zeros at infinity

**Physics Forums | Science Articles, Homework Help, Discussion**