Boundary and interface function method for one dimensional neutron transport

TL;DR: The theory shows that a rather simple numerical method for the solution of the transport equation is feasible which uses only edge- and interface function approximations and no interior space points in the main program, which drastically reduces the order of the associated matrix problem as well as improving the computational execution time on the computer.

Abstract: A new numerical method, the Boundary and Interface Function (BIF) Method, for solving the one-dimensional neutron transport equation is formulated. The method derives its mathematical foundation from a two-sided Laplace transform in the space variable with a Fourier transform in the angular variable. The mathematical solution requires that the scalar flux at the boundaries and interfaces (the boundary and interface functions) satisfy systems of singular integral equations. The theory shows that a rather simple numerical method for the solution of the transport equation is feasible which uses only edge- and interface function approximations and no interior space points in the main program. This drastically reduces the order of the associated matrix problem as well as improving the computational execution time on the computer. A computer code has been implemented and numerical results are presented and compared with a reference solution and solutions obtained by conventional methods for one and two region problems.