New in Mathematica 9

Advanced Hybrid and Differential Algebraic Equations

Mathematica 9 extends the broad language of modeling with differential equations to include advanced algorithms for solving differential-algebraic equations and hybrid systems with a mix of continuous- and discrete-time behavior. Automatic detection of discontinuous functions provides accurate solutions for discontinuous differential equations expressed in a natural mathematical specification.

  • Automatic detection and handling of discontinuous solutions.
  • Filippov sliding mode solutions automatically computed when appropriate.
  • New WhenEvent allows flexible specification of arbitrary events and corresponding actions.
  • Discrete state changes expressed naturally through rules in WhenEvent.
  • Variables that only change at discrete times can be added without increasing the differential system size and solving complexity.
  • Advanced support for DAE allows for easier modeling of connected systems.
  • Symbolic graph- and matrix-based index reduction methods for high-index DAEs.
  • Advanced initialization algorithms for DAEs.
  • New solving methods for DAEs.
  • Arbitrary-precision solution of DAEs.

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