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help ode45
ODE45  Solve non-stiff differential equations, medium order method.
    [T,Y] = ODE45(ODEFUN,TSPAN,Y0) with TSPAN = [T0 TFINAL] integrates the
    system of differential equations y' = f(t,y) from time T0 to TFINAL with
    initial conditions Y0. Function ODEFUN(T,Y) must return a column vector
    corresponding to f(t,y). Each row in the solution array Y corresponds to
    a time returned in the column vector T. To obtain solutions at specific
    times T0,T1,...,TFINAL (all increasing or all decreasing), use
    TSPAN = [T0 T1 ... TFINAL].     
   
    [T,Y] = ODE45(ODEFUN,TSPAN,Y0,OPTIONS) solves as above with default
    integration properties replaced by values in OPTIONS, an argument created
    with the ODESET function. See ODESET for details. Commonly used options
    are scalar relative error tolerance 'RelTol' (1e-3 by default) and vector
    of absolute error tolerances 'AbsTol' (all components 1e-6 by default).
   
    [T,Y] = ODE45(ODEFUN,TSPAN,Y0,OPTIONS,P1,P2...) passes the additional
    parameters P1,P2,... to the ODE function as ODEFUN(T,Y,P1,P2...), and to
    all functions specified in OPTIONS. Use OPTIONS = [] as a place holder if
    no options are set.   

    ODE45 can solve problems M(t,y)*y' = f(t,y) with mass matrix M that is
    nonsingular. Use ODESET to set the 'Mass' property to a function MASS if
    MASS(T,Y) returns the value of the mass matrix. If the mass matrix is
    constant, the matrix can be used as the value of the 'Mass' option. If
    the mass matrix does not depend on the state variable Y and the function
    MASS is to be called with one input argument T, set 'MStateDependence' to
    'none'. ODE15S and ODE23T can solve problems with singular mass matrices.  

    [T,Y,TE,YE,IE] = ODE45(ODEFUN,TSPAN,Y0,OPTIONS...) with the 'Events'
    property in OPTIONS set to a function EVENTS, solves as above while also
    finding where functions of (T,Y), called event functions, are zero. For
    each function you specify whether the integration is to terminate at a
    zero and whether the direction of the zero crossing matters. These are
    the three vectors returned by EVENTS: [VALUE,ISTERMINAL,DIRECTION] =
    EVENTS(T,Y). For the I-th event function: VALUE(I) is the value of the
    function, ISTERMINAL(I)=1 if the integration is to terminate at a zero of
    this event function and 0 otherwise. DIRECTION(I)=0 if all zeros are to
    be computed (the default), +1 if only zeros where the event function is
    increasing, and -1 if only zeros where the event function is
    decreasing. Output TE is a column vector of times at which events
    occur. Rows of YE are the corresponding solutions, and indices in vector
    IE specify which event occurred.   

    SOL = ODE45(ODEFUN,[T0 TFINAL],Y0...) returns a structure that can be
    used with DEVAL to evaluate the solution or its first derivative at
    any point between T0 and TFINAL. The steps chosen by ODE45 are returned
    in a row vector SOL.x.  For each I, the column SOL.y(:,I) contains
    the solution at SOL.x(I). If events were detected, SOL.xe is a row vector
    of points at which events occurred. Columns of SOL.ye are the corresponding
    solutions, and indices in vector SOL.ie specify which event occurred.

    Example   
          [t,y]=ode45(@vdp1,[0 20],[2 0]);   
          plot(t,y(:,1));
      solves the system y' = vdp1(t,y), using the default relative error
      tolerance 1e-3 and the default absolute tolerance of 1e-6 for each
      component, and plots the first component of the solution.
   
    Class support for inputs TSPAN, Y0, and the result of ODEFUN(T,Y):
      float: double, single

    See also
        other ode solvers:    ode23, ode113, ode15s, ode23s, ode23t, ode23tb
        options handling:     odeset, odeget
        output functions:     odeplot, odephas2, odephas3, odeprint
        evaluating solution:  deval
        ode examples:         rigidode, ballode, orbitode

    NOTE:
      The interpretation of the first input argument of the ODE solvers and
      some properties available through ODESET have changed in this version
      of MATLAB. Although we still support the v5 syntax, any new
      functionality is available only with the new syntax. To see the v5
      help, type in the command line  
          more on, type ode45, more off

    Reference page in Help browser
       doc ode45
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3Â¥2016-01-07 15:57:18
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