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[求助] ode45已有4人参与

一道常微分求解的题目，要求用四阶龙格库塔法R-K，求Matlab中的ode45算法的内部算法程序代码，或者思路。

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最怜宵舞: 金币+5, ★有帮助 2016-01-07 17:43:17

ode45Matlab自带了，你还确定继续自己写？？

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