A computational framework has been developed for step-by-step implementation of global spectral projection methods used for solving boundary-value problems and analyzing solutions produced using the numerical techniques of this framework. A set of Matlab-based functions corresponding to each step in a Galerkin discretization procedure has been developed with emphasis on simplifying the implementation of discretization methods for nonlinear, distributed-parameter system models in up to three-dimensional physical domains. A key feature of this computational approach is that a set of object classes were developed to facilitate implementation of the weighted residual methods (MWR) in an effort to make the connection between the solution procedures and modeling equations as clear as possible. The utility of the computational procedures is demonstrated through applications to two-dimensional reaction-diffusion and fluid flow problems, and a three-dimensional heat transfer problem in semiconductor manufacturing.