The present work summarizes the theory and describes the algorithm related to the construction of an open source mixed symbolic-numerical computational code named UNIT — Unified Integral Transforms, that provides a development platform for finding solutions of linear and nonlinear partial differential equations via integral transforms. The reported research was performed by making use of the symbolic computational system Mathematica v.7.0 and the hybrid numerical-analytical methodology Generalized Integral Transform Technique — GITT. The aim here is to illustrate the robust and precision controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source code. Test cases are selected based on nonlinear multi-dimensional formulations of the Burgers equations, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects and computational behaviors of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code.
The UNIT algorithm for solving one-dimensional convection-diffusion problems via integral transforms
