Feasibility and Comparison Investigation of the Use of the Fast Fourier Transform and Finite Difference Method for Numerical Solution of Boundary Value Problems.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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This thesis determined the feasibility of using Fast Fourier Transforms FFT to solve Boundary Value Problems BVP and then compare the results to those of the Finite Difference Method FDM. Variations of Poissons one and two dimensional equations were used as a vehicle to develop the FFT method. For the one dimensional BVP, both homogeneous and non-homogeneous Dirichlet boundary conditions were considered. In the one dimensional BVP the inhomogeneous function, Fx, was also varied. The two dimensional BVP, only one inhomogeneous function, Fx,y, and homogeneous boundary conditions were used. The one dimensional model was used as a basis for developing the two dimensional model. The analytical solution of each problem was compared to the numerical solution of the FDM and the FFt method at varying mesh sizes. The computational time of the FDM and the FFT method were also compared. The results indicate that the FFT is extremely efficient in the two dimensional BVP because of the computer storage space required and the computational time needed to solve the FFTs. The accuracy of the FFT compares favorably to the FDM and, as the mesh size decreases, becomes more accurate than the FDM.
- Numerical Mathematics