4阶定步长龙格库塔法

function Y = ode4(odefun,tspan,y0,varargin)
%ODE4 Solve differential equations with a non-adaptive method of order 4.
% Y = ODE4(ODEFUN,TSPAN,Y0) with TSPAN = [T1, T2, T3, ... TN] integrates 
% the system of differential equations y' = f(t,y) by stepping from T0 to 
% T1 to TN. Function ODEFUN(T,Y) must return f(t,y) in a column vector.
% The vector Y0 is the initial conditions at T0. Each row in the solution 
% array Y corresponds to a time specified in TSPAN.
%
% Y = ODE4(ODEFUN,TSPAN,Y0,P1,P2...) passes the additional parameters 
% P1,P2... to the derivative function as ODEFUN(T,Y,P1,P2...). 
%
% This is a non-adaptive solver. The step sequence is determined by TSPAN
% but the derivative function ODEFUN is evaluated multiple times per step.
% The solver implements the classical Runge-Kutta method of order 4. 
%
% Example 
% tspan = 0:0.1:20;
% y = ode4(@vdp1,tspan,[2 0]); 
% plot(tspan,y(:,1));
% solves the system y' = vdp1(t,y) with a constant step size of 0.1, 
% and plots the first component of the solution. 
%

if ~isnumeric(tspan)
error('TSPAN should be a vector of integration steps.');
end

if ~isnumeric(y0)
error('Y0 should be a vector of initial conditions.');
end