*SP*_{1}and*P*_{1}equations are identical.*SP*_{N}and*P*_{N}equations are identical in 1-D slab geometry.- Rotationally invariant no ray effects.
*SP*_{N}is a non-convergent method. It is an asymptotic approximation associated with the diffusion limit. As*N*, the solution doesn't necessarily converge to the true answer.*SP*_{N}has almost the same accuracy for lower orders as*S*_{N}if the solution is approximately locally 1-D, but is much cheaper.- With DSA and LMFG acceleration,
*SP*_{N}costs*MG*+*G*+ 1 diffusion solutions for every outer iteration. - Unlike the diffusion equation, the
*SP*_{N}equations propagate information at a finite speed. For radiation, this speed approaches*c*from below as the order of approximation is increased. - Order
*N*unknowns for*SP*_{N}, vs. order*N*^{2}unknowns for*P*_{N}and*S*_{N}. - In a homogeneous region,
*SP*_{N}and*P*_{N}scalar flux solutions satisfy same equation, except with different boundary conditions.