Abstract
Publisher Summary This chapter discusses the methods employed for the solution of the transport equation in slab geometry, transformation of the monoenergetic transport equation, a round-off free solution for the monoenergetic one-velocity single-region transport equation, the multi-region solution of the slab problem, and applications of the round-off free solution. The nuclear engineer or shield designer usually associates the Monte Carlo method with very long computing times. It turns out that at large distances from the source, very few particles can be expected to reach and to be recorded in some specific angular direction or energy range. For a reliable statistical answer, a sufficient number of particles are needed. This necessitates the tracing of the histories of an immensely large number of particles. Techniques like biased sampling and splitting and Russian roulette that increase the probability of an initial particle contributing to the final answer have been used to considerably decrease the time required for a solution. Monte Carlo calculations are resorted to only when the complications of geometry of the source and the region make it impossible to find an answer by other means. This method is particularly useful for the calculation of integral rather than differential quantities.
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