Book Description

The solution of the nonlinear two-dimensional reactor dynamics equation subjected to prompt feedback conditions using the finite element technique leads to a matrix formulation. The task of this thesis is the development of computational techniques which allow the problem to be solved for large systems. Specifically, these techniques are: (1) the treatment of the nonlinearity on the element level, (2) the compacting of the sparce matrices to include only non-zero terms, and (3) the construction of a new computer code based on the Crank-Nicolson formulation for the solution of differential equations. To support the theory presented, test problems were solved by the original method, the linearized technique, and the Crank-Nicolson treatment. The results were analyzed and compared graphically. All three of the innovations developed in this thesis appear to be useful tools for solving nonlinear time dependent differential equations.