matlab ode45 函数传自定义参数用法及定步长ode5解算函数
%程序1arg1 = 2;
arg2 = 1;
= ode45('vdp1000',,, [], arg1, arg2);
plot(T,Y(:,1),'-o');
%%程序2
function dy = vdp1000(t, y, flag, arg1, arg2)
dy = zeros(2,1); % a column vector
dy(1) = y(2);
dy(2) = arg1*(arg2 - y(1)^2)*y(2) - y(1);
%%ode5
function Y = ode5(odefun,tspan,y0,varargin)
%ODE5 Solve differential equations with a non-adaptive method of order 5.
% Y = ODE5(ODEFUN,TSPAN,Y0) with TSPAN = 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 = ODE5(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 Dormand-Prince method of order 5 in a general
% framework of explicit Runge-Kutta methods.
%
% Example
% tspan = 0:0.1:20;
% y = ode5(@vdp1,tspan,);
% 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
h = diff(tspan);
if any(sign(h(1))*h <= 0)
error('Entries of TSPAN are not in order.')
end
try
f0 = feval_r(odefun,tspan(1),y0,varargin{:});
catch
msg = ['Unable to evaluate the ODEFUN at t0,y0. ',lasterr];
error(msg);
end
y0 = y0(:); % Make a column vector.
if ~isequal(size(y0),size(f0))
error('Inconsistent sizes of Y0 and f(t0,y0).');
end
neq = length(y0);
N = length(tspan);
Y = zeros(neq,N);
% Method coefficients -- Butcher's tableau
%
% C | A
% --+---
% | B
C = ;
A = [ 1/5, 0, 0, 0, 0
3/40, 9/40, 0, 0, 0
44/45 -56/15, 32/9, 0, 0
19372/6561, -25360/2187, 64448/6561, -212/729, 0
9017/3168, -355/33, 46732/5247, 49/176, -5103/18656];
B = ;
% More convenient storage
A = A.';
B = B(:);
nstages = length(B);
F = zeros(neq,nstages);
Y(:,1) = y0;
for i = 2:N
ti = tspan(i-1);
hi = h(i-1);
yi = Y(:,i-1);
% General explicit Runge-Kutta framework
F(:,1) = feval_r(odefun,ti,yi,varargin{:});
for stage = 2:nstages
tstage = ti + C(stage-1)*hi;
ystage = yi + F(:,1:stage-1)*(hi*A(1:stage-1,stage-1));
F(:,stage) = feval_r(odefun,tstage,ystage,varargin{:});
end
Y(:,i) = yi + F*(hi*B);
end
Y = Y.';
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