As the complexity of modern engineering systems increases, Mathematica's unique breadth and integration becomes ever more important for dynamic simulation. With its symbolic architecture, document-centered interface and built-in access to the world's largest web of state-of-the-art algorithms, Mathematica provides a uniquely effective platform for constructing, implementing, documenting and analyzing complex simulations.
Mathematica's algorithmic breadth and unified design—consistently covering both established and emerging modeling methodologies, including ODEs, PDEs, DAEs, CAs, discrete systems, optimization and much more—give modern model builders unique flexibility in selecting and seamlessly combining the best modeling frameworks. Wolfram Research has long been a leader in developing new solver technologies, and Mathematica's unique automated algorithm selection methodology dynamically picks the best state-of-the-art algorithms at all stages in a simulation.
While traditional simulation systems tend to focus on particular areas, Mathematica not only provides broad multiparadigm modeling and computation, but also includes unique support for the complete simulation project workflow. With its immediate interactive interface, powerful built-in programming and development environment, world-class visualization, custom dynamic interface construction system, rich built-in documentation and presentation system, and broad connectivity to external systems, Mathematica allows a new level of productivity in simulation-oriented projects.
While earlier-generation simulation systems tend to be based on hand-constructed block diagrams, Mathematica emphasizes more systematic equation, program and language-oriented approaches. Mathematica's unique symbolic architecture allows it to offer a wide range of increasingly important capabilities that can never be coherently achieved with traditional simulation systems, including algebraic model derivation and verification, integrated perturbation analysis and parameter optimization, full algorithmic model construction, symbolic model validation and full meta-analysis and encapsulation of models.