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.

$\mathrm{with}\left(\mathrm{Matlab}\right)\:$

$T,Y≔\mathrm{ode45}\left(''vdp1''\,0..20\,\left[2\,0\right]\right)$

$T,Y≔\mathrm{ode15s}\left(''vdp1000''\,0..30\,\left[2\,0\right]\right)$

$\mathrm{file}≔\mathrm{open}\left(''C:MATLABwork\backslash rocket.m''\,\mathrm{WRITE}\right)\:$

$\mathrm{writeline}\left(\mathrm{file}\,\mathrm{filecontents}\right)\:$

$\mathrm{close}\left(\mathrm{file}\right)\:$

$\mathrm{ssystem}\left(''chmod\; a+r\; rocket.m''\right)\:$

$\mathrm{with}\left(\mathrm{Matlab}\right)$

$\mathrm{evalM}\left(''open(\text{'}C:MATLABwork\backslash rocket.m\text{'})''\right)\:$

$\mathrm{setvar}\left(''DMIN''\,0.5\,'\mathrm{globalvar}'\right)$

$\mathrm{setvar}\left(''INTERCEPT''\,\mathrm{\infty }\,'\mathrm{globalvar}'\right)$

$\mathrm{ti}≔0\:$

$\mathrm{tf}≔20\:$

$\mathrm{Yo}≔\left[0\,0\,0\right]\:$

$T,Y≔\mathrm{ode45}\left(''rocket''\,\mathrm{ti}..\mathrm{tf}\,\mathrm{Yo}\,'\mathrm{tol}'=0.0005\right)\:$

$\mathrm{pursuer\_plot}≔\mathrm{plots}\left[\mathrm{pointplot3d}\right]\left(\mathrm{convert}\left(Y\,\mathrm{listlist}\right)\,\mathrm{color}=\mathrm{blue}\,\mathrm{symbol}=\mathrm{diamond}\right)\:$

$\mathrm{target\_plot}≔\mathrm{plots}\left[\mathrm{pointplot3d}\right]\left(\left[\mathrm{seq}\left(\left[10\,t\,0\right]\,t=\mathrm{ti}..10\right)\,\mathrm{seq}\left(\left[10\,10\,t-10\right]\,t=10..\mathrm{tf}\right)\right]\,\mathrm{color}=\mathrm{red}\,\mathrm{symbol}=\mathrm{cross}\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(\left\{\mathrm{pursuer\_plot}\,\mathrm{target\_plot}\right\}\,\mathrm{axes}=\mathrm{normal}\right)$