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Planned Future Development

Development of NodePy is based on research needs. The following is a list of capabilities or features that would naturally fit into the package but have not yet been implemented.

Multistep methods

  • Time-stepping for multistep methods
  • Selection of startup method
  • Variable step size multistep methods
  • Properties of particular multistep + startup method combinations
  • Adaptive step size and order selection

Runge-Kutta Methods

  • Time stepping for implicit methods
  • Interpolants (dense output)
  • Adaptive order (extrapolation and deferred correction)

PDEs

Many common semi-discretizations of PDEs will be implemented as \(ivp\) objects. Initially this will be implemented purely in Python and limited to simple 1D PDEs (e.g. advection, diffusion), since time-stepping for multi-dimensional or nonlinear PDEs will be too slow in Python. Eventually we plan to support wrapped Fortran and C semi-discretizations.

Miscellaneous

  • Additional classes of multi-stage, multistep methods.
  • Analysis of geometric integrators.
  • Partitioned rooted trees, additive and partitioned RK methods.
  • Unit tests.
  • An automatically-generated encyclopedia of solvers.

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