An Approximate Calculation Method of the λ, ωp and ωd Eigenvalue Problem of the Group Diffusion Equation
Hidekazu Yoshikawa, Jiro Wakabayashi · Journal of Nuclear Science and Technology · 1970
The approximate solutions of the, λ, ω p and ω d eigenvalue problems of the group-diffusion equation for a multi-region reactor are obtained by expanding neutron fluxes into finite numbers of eigenfunctions satisfying the Helmholtz equation and the boundary condition at the extrapolated boundary of the reactor. The original eigenvalue problem is reduced to that of an asymmetric real matrix for the vector whose components constitute the expansion coefficients. For the numerical calculation of the real matrix thus derived, to determine the higher λ, ω p and ω d modes, the QR iteration method based on numerically stable unitary transformation, in combination with inverse iteration is effective in saving computation time. The λ, ω p and ω d modes obtained by the above method are expressed by a linear combination of a comparatively small number of simple elementary functions, and are thus of high practical value in the numerical calculation of higher order perturbations and for examining snace-deDendent reactor dynamics.