- #1
omyojj
- 37
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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.
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.