Richardson extrapolation of a positive method for numerically solving the transport equation in spherical geometry
Abbott, William Ervin
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This thesis presents a positive method for numerically solving the neutron transport equation in spherical geometry. The method is shown to have an asymptotic error expansion allowing the use of Richardson extrapolation to improve the numerical results. Numerical results for the method are presented for several spherical models. These results are compared to exact solutions where possible and to numerical results from standard nonpositive difference methods. In addition, a convergence analysis is presented for the method.