====== NDF ======

Implicit multistep-solver of variable order (1-5) based on the Numerical Differentiation Formulas (NDFs).

Applicable for **stiff** problems of **low** to **medium** accuracy.

For some ODE problems, the step size taken by the solver is forced down to an unreasonably small level in comparison to the interval of integration, even in a region where the solution curve is smooth. These step sizes can be so small that traversing a short time interval might require millions of evaluations. This can lead to the solver failing the integration, but even if it succeeds it will take a very long time to do so.

Equations that cause this behavior in ODE solvers are said to be stiff.

Applicable [[Solver_settings|solver settings]]:

  * Absolute tolerance
  * Relative tolerance
  * Initial step size
  * Max step size
  * Min step size
  * Refine
  * Limit data points to last
  * Norm Control
  * Allowed step size violations
  * Enable saturation
  * Max order
  * LU decomposition matrix format

===== Reference =====

  * Shampine, L. F. and M. W. Reichelt, “The MATLAB ODE Suite,” //SIAM Journal on Scientific Computing//, Vol. 18, 1997, pp 1-22.
  * Shampine, L. F., M. W. Reichelt, and J.A. Kierzenka, “Solving Index-1 DAEs in MATLAB and Simulink,” //SIAM Review//, Vol. 41, 1999, pp 538-552.