Comparing software for interactive solution of systems of nonlinear algebraic equations

Four general purpose interactive numerical solution packages: MAPLE, MATLAB, MATHEMATICA and POLYMATH are compared with regard to their performance in solving systems of nonlinear algebraic equations typical to chemical engineering applications. Criteria for ease of learning, ease of use and user-friendliness of the packages are introduced. Benchmark problems are used to demonstrate that the selection of good initial estimates is still a critical issue in solving highly nonlinear problems with any of these programs. It is concluded that of the programs tested, the performance of MATHEMATICA and POLYMATH is the best for systems of NLEs, the interval of convergence of POLYMATH and MAPLE is the widest for a single NLE and POLYMATH possesses the most "user-friendly" features.