Investigation of the Numerical Method of Moments for Digital Computer Determination of Differential Equations.
Abstract
The purpose of this thesis was to determine the feasibility of using the method of weighted residuals to obtain approximations to the discrete Green's function, or analogs to it. The weighted residual methods of Galerkin and collocation, as well as the finite difference method were programmed of a Kaypro II micro-computer in Microsoft Basic. These programs were used to generate approximations to the one- and two-dimensional Poisson's equation, The two-dimensional case was restricted to the geometry of a unit square. Various inhomogeneity terms were used to obtain approximate solutions to the discrete Green's functions or their analogs. The results were compared with the analytical values at various interior nodal points on the mesh. The average percent error for the approximations were reported for each case as the number of interior nodal points was increased. The areas of consideration were the rate of convergence to the analytical solution, the amount of time it took to run each program, and the accuracy of the approximate solutions. The results of this study indicate that the Green's functions or analogs obtained are valid approximations to the discrete Green's functions or analogs obtained are valid approximations to the discrete Green's functions. The method of weighted residuals proved to be very sensitive to the choice of basis functions, resulting in ill-conditioned matrices in some instances. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1984
- Accession Number
- ADA151896
Entities
People
- D. E. Oyler
Organizations
- Air Force Institute of Technology