Date of Award
Doctor of Philosophy
Analyses have been made of the truncation error for the following finite difference approximations to the eigenvalue and boundary value problems evolving from the one-group neutron diffusion equation: (i) The seven-point relation; (ii) The fifteen-point relation; (iii) The nineteen-point relation; and (iv) The twenty-seven point relation. These methods have been derived using a Taylor series expansion technique and applied to the Laplacian operator contained in that equation in (x,y,z) geometry for various reactor configurations and boundary conditions;It has been shown that for methods ii and iii, a 4th order truncation error can be achieved, whereas for the 27-point approximation, a 6th order truncation error is possible;From the computer results of sample problems, considerable savings in accuracy (accurate eigenvalue and/or eigenfunctions) and system memory (fewer number of meshes required) can be obtained using the high order approximations, especially the 27-point relation, as compared to the 2nd order approximation.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Benghanem, Mohammed, "Formulation and analysis of higher order finite difference approximations to the neutron diffusion equation " (1986). Retrospective Theses and Dissertations. 8140.