Gauss numerical integration is applied to compute the radial emission coefficients in Optically-Thick,Cylindrically-Symmetric Plasmas.Using the integration,the generalized Abel equation is separated into a system of linear algebraic equations and the coefficient matrix of the system is an upper triangular matrix,so the interpolation,which has second order of accuracy,is very simple to compute and less computation time is required.

Classical trajectories of diatomic system N₂ are calculated by means of both Symplectic and R-K algorithms.It is shown that Symplectic algorithm keeps Symplectic structure of the system and its intrinsic qualities unchanged and consistent with the theory and experiment. R-K approach is not the case.

A difference quotient-numerical integration method is adopted to solve radiative transfer problems in an anisotropic scattering slab medium. By using the method, the radiative transfer problem is separated into a system of linear algebraic equations and the coefficient matrix of the system is a band matrix, so the method is very simple to evaluate on computer and to deduce formulae and easy to master for experimentalists. An example is evaluated and it is shown that the method is precise.