The discussion focuses on modeling a star using the shooting method and the multi-dimensional Newton-Raphson technique. The user encountered issues during the integration process and seeks clarification on applying the Newton-Raphson method correctly. Key steps include starting with the equations of stellar structure, applying boundary conditions, and utilizing the Saha equation for ion abundance. The conversation emphasizes the importance of iterative methods, such as the Runge-Kutta technique, to achieve convergence in density functions.
PREREQUISITESAstronomy students, astrophysicists, and computational scientists involved in stellar modeling and numerical methods.
Start with the equations of stellar structure and the equation of hydrostatic equilibrium, apply the boundary conditions you know: core temperature and pressure, and T=0 and P=0 at r=Rsun. The XYZ composition and the Saha equation gives you the abundance of free ions and the opacity. Use the chain rule to change the independent variable from radius fraction to mass fraction. Begin by assuming constant density. Solve the equation set to obtain a revised density function, and repeat until rho(M) converges. Runga Kutta might give you the power fraction enclosed from M=0 to M=Mi. If there's a name for doing this, I never heard what it was.mccizmt2 said:I am trying to model a star using the old shooting method technique. I've encountered problems after my very first pass of integration. I know that I need to use a multi-dimensional Newton-Raphson technique and i think that I've not done this correctly. Could anybody please try and explain this technique.