P_N Calculations

A method of doing P_N calculations which is particularly useful for classroom use is presented. The method is basically a systematic numerical implementation of the analytic method of characteristic solutions. The extensive tabulations of characteristic roots are used as guide lines for the solution of the characteristic (N + 1) order polynomial equation. Then the tables of coupling coefficients are used to guide the evaluation of the coupling or recursion relations. The systematics of matrix algebra is next used to set up the linear equations resulting from the boundary conditions and to reconstruct the angular moments and the angular fluxes. The use of these tabulated guide lines and matrix operations to provide the single and double summations reduces the problem to a very managable level. A sample P₃ problem treated in this manner is presented.