# Summary

Using DEQSOL to integrate and fit differential equations

DEQSOL will integrate and fit systems of nonlinear differential equations dy(i)/dx defined either in the Simfit compiled library, or supplied by users as ASCII text model files.
Initial conditions, values for model parameters, and an integration range must be supplied.

Note that, in this version, initial conditions are assumed to refer to x = 0, the integration is restricted to x >= 0, and the solution will always be advanced from x = 0, no matter what range of integration is requested, or what range of x is included in the data for fitting.
To be precise:

- Let [x_{1s}, x_{ns}] be the range to simulate ns points xs, i.e.
  0 =< x_{1s} =< xs =< x_{ns}
- Let [x_{1d}, x_{nd}] be the range set by nd data values xd, i.e.
  0 =< x_{1d} =< xd =< x_{nd}
- Define x_{start} = min(x_{1s}, x_{1d}), and x_{end} = max(x_{ns},x_{nd}).
  Then the integration range will be [x_{start}, x_{end}], i.e.
  0 =< x_{start} =< x =< x_{end}
  but the initial conditions will be assumed to refer to x = 0, if x_{start} > 0.

Users must understand the mathematics of the model of interest, and must must be familar with the concepts involved in this area, such as stifness, initial conditions, Jacobians, orbits, autonomous systems, convergence, etc.
The program can plot profiles, orbits, and phase diagrams, etc. and can fit data supplied as library files referencing Simfit data files for such components of the system as have been sampled.
Subsets of data can be fitted if not all of the components have been sampled experimentally, by simply using a percentage sign in the library file.

Back to Help Menu or End Help