瀹為獙鍥?/p>
甯稿井鍒嗘柟绋嬬殑鏁板�艰В娉?/p>
鎸囦护锛?/p>
[t,y]=ode23(
鈥?/p>
fun
鈥?/p>
,tspan,yo)
2/3
闃堕緳鏍煎簱濉旀柟娉?/p>
[t,y]=ode45(
鈥?/p>
fun
鈥?/p>
,tspan,yo)
4/5
闃堕緳鏍煎簱濉旀柟娉?/p>
[t,y]=ode113(
鈥?/p>
fun
鈥?/p>
,tspan,yo)
楂橀樁寰垎鏂圭▼鏁板�兼柟娉?/p>
鍏朵腑
fun
鏄畾涔夊嚱鏁扮殑鏂囦欢鍚嶃�?/p>
璇ュ嚱鏁?/p>
fun
蹇呴』浠ヤ负
dx
杈撳嚭閲忥紝
浠?/p>
t,y
涓鸿緭鍏ラ噺銆?/p>
tspan=[t0
tfina]
琛ㄧず绉垎鐨勮捣濮嬪�煎拰缁堟鍊笺�?/p>
yo
鏄垵濮嬬姸鎬佸垪鍚戦噺銆?/p>
鑰冭檻鍒板垵濮嬫潯浠舵湁
0
0
d
,
(0)
0,
d
d
,
(0)
0.
d
S
SI
S
S
t
I
SI
I
I
I
t
飦?/p>
飦?/p>
飦?/p>
飪?/p>
飥?/p>
飥?/p>
飥?/p>
飥?/p>
飪?/p>
飪?/p>
飪?
飪?/p>
飥?/p>
飥?/p>
飥?/p>
飩?/p>
飪?/p>
飪?/p>
(5.24)
杩欏氨鏄?/p>
Kermack
涓?/p>
McKendrick
鐨?/p>
SIR
浠撳妯″瀷
.
鏂圭▼
(5.24)
鏃犳硶姹傚嚭
(
)
S
t
鍜?/p>
(
)
I
t
鐨勮В鏋愯В
.
鎴戜滑鍏堝仛鏁板�艰绠椼�?/p>
Matlab
浠ｇ爜涓猴細
function
dy=rigid(t,y)
dy=zeros(2,1);
a=1;
b=0.3;
dy(1)=a*y(1).*y(2)-b*y(1);
dy(2)=-a*y(1).*y(2);
ts=0:.5:50;
x0=[0.02,0.98];
[T,Y]=ode45(
'rigid'
,ts,x0);
%plot(T,Y(:,1),'-',T,Y(:,2),'*')
plot(Y(:,2),Y(:,1),
'b--'
)
xlabel(
's'
)
ylabel(
'i'
)
浠诲姟锛?/p>
1
鐢诲嚭
i
锛?/p>
t
锛?/p>
锛?/p>
2
鍒嗘瀽鍚勫弬鏁扮殑褰卞搷
渚?/p>
57
锛氭眰瑙ｄ袱鐐硅竟鍊奸棶棰橈細
0
)
5
(
,
0
)
1
(
,
3
2
飥?/p>
飥?/p>
飥?/p>
飩?/p>
飥?/p>
飩?/p>
飩?/p>
y
y
x
y
y
x
銆傦紙娉ㄦ剰锛氱浉搴旂殑鏁板�艰В娉?/p>
姣旇緝澶嶆潅锛夈�?/p>
y=dsolve('x*D2y-3*Dy=x^2','y(1)=0,y(5)=0','x')
鈫?/p>
y =
-1/3*x^3+125/468+31/468*x^4