Mathematical solutions of the one-dimensional neutron transport equation
Davis, Larry Thomas
Garrettson, Garrett A.
MetadataShow full item record
Considering the case of one speed, steady state, isotropic scattering in homogeneous media with plane symmetry, this thesis developes the solution of the one-dimensional neutron transport equation by three separate techniques The method of K. M. Case which makes use of the theory of generalized functions in forming a semi-classical eigenfunc- tion expansion with both a continuous spectrum and a finite discrete spectrum is developed. Converting the neutron transport equation to an integral equation and then to a singular integral equation, a solution is found in a method due to T. W. Mullikin which has very useful convergence properties. Applying the method due to N. Weiner and E. Hopf to the integral equation form of the neutron transport equation, a solution is developed which depends heavily on complex variable theory. The similarities, differences, advantages and disadvantages in the three methods are pointed out, and specific example solutions are presented.
Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations Kang, Wei; Wilcox, Lucas C. (Springer, 2017-04-08);We address finding the semi-global solutions to optimal feedback control and the Hamilton–Jacobi–Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time ...
Harris, Leonard H. (Monterey, California: U.S. Naval Postgraduate School, 1961);This paper presents a new numerical method for solving Schroedinger 's equation in radial form in order to get a set of wave functions for use as starting values in the solution of the Fock equation. As a necessary ...
Davis, William Joseph (Monterey, California. Naval Postgraduate School, 1968-06);Solutions to a nonlinear wave equation were analyzed for their stability. The wave equation is a Klein-Gordon equation with the mass replaced by the square of the wave function. This wave equation has propagating solutions ...