The ode45 command uses MATLAB to compute the ODE45 solution of a differential system. The ode15s command uses MATLAB to compute the ODE15S solution of a differential system.

To be valid, the call must name the function (f) defined in MATLAB, and specify both the time range (Trange) and the initial condition vector (IC).

The function f must either be a built-in MATLAB function, or a function defined in the file f.m in the active MATLAB path

The time range must contain both a start time (t_initial) and an end time (t_final).

The initial condition (IC) must have a dimension consistent with the dimension of the system defined in the function, f.

The tolerance option (specified using 'tol'=Tol) must be a floating-point value.  It defaults to .001 if not specified.

Executing the ode45 command returns two Vectors: (T, X). T is the Vector of time steps where f was evaluated, and X is a Vector of values of f, evaluated at times in T.