Algorithms to Approximate Solutions of Poisson\u27s Equation in Three Dimensions

The focus of this research was to develop numerical algorithms to approximate solutions of Poisson\u27s equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson\u27s equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested with an increasing number of subintervals to ensure that the approximations get closer to the actual solution