On the Analytical Solution of the Multi-Group Neutron Diffusion Kinetic Equation in One-Dimensional Cartesian Geometry by an Integral Transform Technique
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The Generalized Integral Transform Technique, henceforth named GITT approach, is a well established methodology to solve analytically linear differential equations for a broad class of problems in the area of physics and engineering. By analytical we mean that no approximation is done along the derivation of the solution, except for the truncation of the solution series in numerical computations. The main idea of this approach relies on the construction of a pair of transformations from the Laplacian adjoint terms appearing in the differential equation to be solved. This fact allows us to write the solution as a series expansion in terms of the orthogonal eigenfunctions obtained from the solution of an auxiliary Sturm–Liouville problem constructed from the adjoint terms.
KeywordsThermal Neutron Fast Neutron Liouville Problem Matrix Differential Equation Coordinate Research Project
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