Description

Fitting the solutions of a set of Ordinary Differential Equations (ODEs) is not so straight forward and the information provided here is just a brief introduction to the subject for a fitteia user. This implies that we focus on the possibility of writing a set of ODEs and to perform a fit/plot of the numerical solutions of one or multiple data sets.

The fitteia's internal fitting function results from the interpretation of a macro function NODE1 representing a system of N ODEs of the 1st order.

NODE1

SYNTAX:

y=NODE1(t, t0, x0, y0, z0, h, "f1", "f2", "f3", ..., k)

• t : independent variable [ex. time]
• t0: is a parameter, usually fixed [initial value of t]
• x0: is a parameter [value of x for t0]
• y0: is a parameter [value of y for t0]
• z0: is a parameter [value of z for t0]
• h : is a parameter [Runge-Kutta step of variable t]
• f1: string [derivative of x with respect to t (dx/dt), x is a dependent variable]
• f2: string [derivative of y with respect to t (dy/dt), y is a dependent variable]
• f3: string [derivative of z with respect to t (dz/dt), z is a dependent variable]
• k : parameter or variable [is an optional index that allows the user to choose which solution is returned by NODE1 (defaults to 1 if ommited). Here k values 1, 2, 3 makes NODE1 to return the value of x, y, or z for the value of t, respectively]

NODE1 provides the solution of differential equations identified by the variable on the left-hand side of the equation. In the equation presented here, this variable is y but you can choose either x or z. This behavior can be modified by the value of index k (the last argument of NODE1 macro). The use of k allows the simultaneous fitting of data corresponding to different dependent variables.

Examples