(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 - The Fusion of Science and Community**

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

Loading...

Similar Threads - Second initial conditions | Date |
---|---|

I Resolution of a PDE with second order Runge-Kutta | Oct 3, 2017 |

I Question about second order linear differential equations | Aug 21, 2017 |

I Second order PDE with variable coefficients | Jul 18, 2017 |

I Constructing a 2nd order homogenous DE given fundamental solution | May 13, 2017 |

Transfer function with non zero initial conditions | Jan 13, 2016 |

**Physics Forums - The Fusion of Science and Community**