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Matlab

  

ode45

  

use MATLAB(R) to solve a previously defined system, f, with ODE45

  

ode15s

  

use MATLAB(R) to solve a previously defined system, f, with ODE15s

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ode45(f, Trange, IC)

ode45(f, Trange, IC, tol=Tol)

ode15s(f, Trange, IC)

ode15s(f, Trange, IC, tol=Tol)

Parameters

f

-

string naming a function defined in MATLAB®

Trange

-

range, t_initial..t_final

IC

-

initial conditions vector; for example, [0, 0, 0]

tol=Tol

-

optional floating-point setting for tolerance (default is .001)

Description

• 

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.

Examples

withMatlab:

Call ode45 to work on a built-in MATLAB® function.

T,Yode45vdp1,0..20,2,0

Call ode15s to work on a built-in MATLAB® function.

T,Yode15svdp1000,0..30,2,0

Create a user-defined function, rocket, in Maple.  The file may also be predefined in the current path.

fileopenC:MATLABwork\rocket.m,WRITE:

filecontents\nfunction yp = rocket(t,y)\n% time the rocket catches the target\nglobal INTERCEPT;\n% minimum distance representing intercept\nglobal DMIN;\n% ratio of pursuer speed to target speed\nk=1.3;\n% find speed and position of target\n% (other equations can be substituted here)\nif t < 10 % target changes direction after 10 seconds\n p = [ 10; t; 0 ];\n vt = [ 0 ; 1; 0 ];\nelse\n p = [ 10; 10; t-10 ];\n vt = [ 0 ; 0; 1 ];\nend\nd = sqrt(sum((p-y).^2)); % calculate distance between P and T\nif d < DMIN % check if pursuer has caught targetN\n if t < INTERCEPT % if this is the first time, set the\n INTERCEPT = t; % interception time\n end\n k = 1; % slow down the pursuer\nend\nvp = k*sqrt(sum(vt.^2)); % set speed of pursuer\nyp = vp*(p-y)/d; % determine new position of pursuer\n&colon;

writelinefile&comma;filecontents&colon;

closefile&colon;

Use the ssystem command to set the permissions on UNIX systems.

ssystemchmod a+r rocket.m&colon;

Open the "Matlab Link".

withMatlab

Before accessing the user-defined function, the file needs to be opened (in MATLAB®).

evalMopen('C:MATLABwork\rocket.m')&colon;

Set global variables (in MATLAB®).

setvarDMIN&comma;0.5&comma;globalvar

setvarINTERCEPT&comma;&comma;globalvar

Setup the problem.

ti0&colon;

tf20&colon;

Yo0&comma;0&comma;0&colon;

Solve the problem.

T,Yode45rocket&comma;ti..tf&comma;Yo&comma;tol=0.0005&colon;

Plot the results.

pursuer_plotplotspointplot3dconvertY&comma;listlist&comma;color=blue&comma;symbol=diamond&colon;

target_plotplotspointplot3dseq10&comma;t&comma;0&comma;t=ti..10&comma;seq10&comma;10&comma;t10&comma;t=10..tf&comma;color=red&comma;symbol=cross&colon;

plotsdisplaypursuer_plot&comma;target_plot&comma;axes=normal

See Also

dsolve

Matlab

Matlab[evalM]

MatlabMatrix