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A NUMERICAL INVESTIGATION AND UTILIZATION OF GREEN'S FUNCTIONS.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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The Greens functions for the Laplacian operator and the modified Helmholtz equation were obtained numerically, for a two-dimensional square, using a finite difference approach. The discrete Greens functions were then employed to obtain numerical solutions, in summation form, for the Laplaces, Poissons, and diffusion equations for a square, subject to Dirichlet boundary conditions. Comparative studies with analytical methods showed the numerical determination of the Greens functions to be a rapid and accurate method. When used to solve the above mentioned equations, the summation process proved to be as accurate and, in some cases, more rapid than the fastest iterative techniques. Author
APPROVED FOR PUBLIC RELEASE