matlab中ode45函数编写.pdf
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function varargout = ode45(ode,tspan,y0,options,varargin)
%ODE45 Solve non-stiff differential equations, medium order method.
% [TOUT,YOUT]= ODE45(ODEFUN,TSPAN,Y0) with TSPAN = [T0 TFINAL] integrates
% the system of differential equationsy' = f(t,y) from time T0 to TFINAL
% with initial conditions Y0. ODEFUN is a function handle. For a scalar
T
% and a vector Y, ODEFUN(T,Y) must return a column vector corresponding
% to f(t,y). Each row in the solution array YOUT corresponds to a time
% returned in the column vector TOUT. To obtain solutions at specific
% times T0,T1,...,TFINAL (all increasing or all decreasing), use TSPAN =
% [T0 T1 ... TFINAL].
%
% [TOUT,YOUT] = ODE45(ODEFUN,TSPAN,Y0,OPTIONS) solves as above with
default
% integrationproperties replaced by values in OPTIONS, an argument created
% with the ODESET function. See ODESET for details. Commonly used options
% arescalar relative error tolerance 'RelTol' (1e-3 by default) and vector
% of absolute error tolerances 'AbsTol' (all components 1e-6 by default).
% If certain components of the solution must be non-negative, use
% ODESET to set the 'NonNegative' property to the indices of these
% components.
%
% 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 handle
% MASSif 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.
%
% [TOUT,YOUT,TE,YE,IE]= ODE45(ODEFUN,TSPAN,Y0,OPTIONS) with the 'Events'
% property in OPTIONS set to a function handle 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 column 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 ODE45are returned
% in a row vector SOL.x. For each I, the column SOL.y(:,I) contains
% thesolution 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
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