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:

• 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

• 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.