Abstract
The monoenergetic integral transport equation in a cylindrical geometry is converted into a system of linear equations by use of the Gaussian quadrature formula, and neutron flux is obtained by solving this system by means of an elimination method using a digital computer. Since the application of n-point Gaussian quadrature formula is equivalent to approximating the integrand by a polynomial of degree 2 n − 1, it gives in general higher accuracy with relatively few sample points than the trapezoidal rule which approximates the integrand by straight lines. In a sample calculation, it becomes apparent that the thermal neutron flux obtained by using the Gaussian quadrature formula in a lattice cell of light water and enriched uranium converges more rapidly with increasing number of sample points than that obtained by using the trapezoidal rule, and 2-point Gaussian formula is comparable with 6-point trapezoidal rule.
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