Numerical solutions to Poisson\u27s equation using radial basis functions

This thesis addresses the problem of obtaining solutions to Poisson\u27s equation which is encountered in the applied sciences and engineering fields. Two separate methods are explained for obtaining particular solutions to this equation. The Method of Fundamental Solutions is then used to solve the remaining homogeneous equation in the context of the Method of Particular Solutions and Dual Reciprocity Method. Numerous examples are given using 2-D and 3-D domain problems; The first method is an interpolation method that has resulted in some problems with ill-conditioning of the matrix used in the problem solving and a remedy has been examined in this paper. The second approximation method is new to this study and has revealed to have excellent results thus far for the problems researched in this paper. The basic theory behind the development of these methods is explained and then examples are given. The examples given were obtained using a Gateway PC with Visual Fortran programming software