Iterative Solutions to the <i>P₁</i> and Double-<i>P¹</i> Equations₁

Abstract

The spherical harmonics approximation of lth order, applied to the transport equation in slab geometry, leads to 2l + 1 coupled first order differential equations. These may be transformed into (2l + 1)/2 second order differential equations similar, in form, to the few-group diffusion equations, and amenable to solution by well-known iterative techniques. The double-P1 equations of Yvon may be manipulated and solved in the same manner. This article describes an IBM 704 code which makes use of such a method. Some of the results obtained with the code are discussed, and machine times for typical problems are compared with times required to solve the same problem by the discrete ordinate methods.