1.1.1. .
1.1.2. .
1.1.3. .
1.1.4. .
1.4. .
1.4.1.
1.4.2. .
1.4.3. .
1.4.4. .
( )
w2 = 2 c = 1
. | . |
--
ode15s ( --), :
y'1 =y2;
y'2 = m*(1y12)*y2y1
y1(0)=0; y2(0)=1.
, LC- , . -- m, . m . μ=100.
ODE-. File ⇒ New ⇒ MMFile
function dydt = vdp100(t,y)
dydt = zeros(2,1); dydt(1) = y(2);
dydt(2) = 100*(1 y(1)^2)*y(2) y(1);
m--.
ode15s (. 8.5) , :
>> [T,Y]=ode15s(@vdp100,[0 30],[2 0]); plot(T,Y)
>> hold on; gtext('y1'), gtext('y2')
y1 = y(1) y2 = y(2) .
. 8.5.
-- y''1 = 2*(1y12)*y1y'1 m = 2. :
y'1 = y2,
y'2 = 2*(1y12)*y1y2.
m- ode- vdp.m:
function [out1,out2,out3] = vdp(t,y,flag)
if nargin < 3 | isempty(flag)
out1 = [2.*y(2).*(1-y(2).^2)-y(1); y(1)];
else
switch(flag)
case 'init' % Return tspan, y0 and options
out1 = [0 20];out2 = [2; 0]; out3 = [ ];
otherwise
error(['Unknown request ''' flag '''.']);
|
|
end
end
ode23 :
>> [T,Y] = ode23(@vdp,[0 20],[2 0]);
>> plot(T,Y(:,1),'-',T,Y(:,2),'-.')
. 8.6. , .
. 8.6.
, , ( ) , , ( ). (), , . , .