m02matlab软件与微分方程模型

1、? ?: · 1 ? ? $?6? .?+) .h? ?m?;? . . .Program andDifferential Equation Ming?<? ? ? ? ?A?n? $?xueyi? ?' 4 ? w ? ?1 1 ? 101 ?JIJJIII K ? ? ? ?)?1 ? ? $?6? .?)?+) .h? ?m?;? . . .1?!1 !1n!1o!? $?6?1?!)?18!1?!?+) .h? ?m?;? ?K? ?' 4 ? w ? ?1 2 ? 101 ?JIJJIII K ? ? ? ? $?1? $?6?1.1.? L?)?+)

2、 .h? ?m?;? . . .1. 1?>>x=-102%?m?m?m% w?(Jx=-1023?% ?"? ?' 4 ? w ? ?1 3 ? 101 ?JIJJIII K ? ? ? ? $?6?2. ?)?+) .h? ?m?;? . . .% L?=?>>yy=382382? ?' 4 ? w ? ?1 4 ? 101 ?JIJJIII K ? ? ? ? $?6?3. ? )?+) .% ;L?1h? ?m?;? . . .>>AA=123;456;780147258360? ?' 4 ? w ? ?1 5 ?

3、101 ?JIJJIII K ? ? ? ? $?6?4. =?)?+) .>>B=Ah? ?m?;? . . .B=123456780? $?1.2.? $?6?3?p0 ? ? $?"? $?)?+) .h? ?m?;? . . .+ 1. ?/ m? ? ?% ? ?7I?10140>>CC=A+ 26B6101410? $? ? A?i?X?6?>>A+2)?+) .ans=3694710582h? ?m?;? . . .? uz? ?+2, ?u?k? (J"X>>x+2ans=124? $?6?2. ?)?+) .

4、? ?Xh? ?m?;? . . .% ? 7I?v? ?5K>>DD=A*B1432233277682368113? $?6?)?$?=X? ?X?+) .h? ?m?;? . . .>>2*A 28ans=41016612014? $?6?, ?k:?$?)?+) .>>C=C=A.*Bh? ?m?;? . . .48L?cij = aij · bij, ?C0= (cij), A = (aij), B = (bij).3. ? ?_% inv?_$?>>inv(A)? $?6?ans=-1.77780.8889-0.1111?)?

5、1.5556-0.77780.2222?+) .h? ?m?;? . . .-0.11110.2222-0.1111? A _? A1. ?d>>I=inv(A)*AI=1.00000.00000.00000.00001.00000001.0000? "? $?6?4. ? ?)?% ?b% ?$?>>>>xb=11b1;?+) .h? ?m?;? . . .xA=-1.00001.00000.0000L?|Ax = b )?=x = A1b.? $?u?|? ?L? ?)?X?6?>>X=1111111111;?)?+) .1y=02

6、03101280;h? ?m?;? . . .>>>>151911;beta=Xybeta=10.20004.0000= = XT X 1 XT y.? $?6?5. ?)?+) .>>D=A2h? ?m?;? . . .D=306639368154154269=D = A2.? $?6? ?k:$?X?)?+) .>>G=G=A.2h? ?m?;? . . .640=gij = a2 , ?G = (gij), A = (aij).ij? $?6?)?>>G=A1.B?+) .h? ?m?;? . . .G =16312526214

7、421871679616116343b=gij = a , ?, A = (a, B = (b.ijG = (g)ijijijij? $?6?| $?|!? ?k? "?1.3.?)?3?+) .h? ?m?;? . . .1. ?|% ;L?w?>>>>xy=14253;6;>>x+yans=579? $?6?)?2. ?|?+) .h? ?m?;? . . .>>z=x4.*y10z=zi=18xi · yi, ?z = (z1, z2, z3), x = (x1, x2, x3), y =(y1, y2, y3).3.

8、?|? $?6?>>z=x.y?)?z=4.00002.50002.0000?+) .h? ?m?;? . . .?L?zi= yi/xi, ?z = (z1, z2, z3), x = (x1, x2, x3),y = (y1, y2, y3).>>z=x./yz=0.25000.40000.5000m?L?zi= xi/yi, ?z = (z1, z2, z3), x = (x1, x2, x3),y = (y1, y2, y3).4. ?|?>>z=x.1y? $?6?z=32729?)?L?zi= xyi,?z= (z1, z2, z3), x= (

9、x1, x2, x3),y=?+) .ih? ?m?;? . . .(y1, y2, y3). , ?k>>z=x.12z=49L?zi = x2, ?z = (z1, z2, z3), x = (x1, x2, x3).i=>>z2.16yz=3264L?zi = 2yi, ?z = (z1, z2, z3), y = (y1, y2, y3).1.4.'X$?u? !?|kXe'X$? $?6? < u u u ?u<=>)?+) .h? ?m?;? . . . >= ?u u= u= ? uXJ'X?K?1?K?0.

10、 X>>a=-124;54-8;>>c=a 01>0c=1110? $?6?1.5.?6$?)?+) .3?kXe?6$?h? ?m?;? . . .& ?| ? ? A & B ?A?B?K? A | B ?A?K? A ?A? ?K? $?6?1.6.? $?)?+) .h? ?m?;? . . .1. ?1 ? ?det()?>>A=123;456;780;>>det(A)ans=272. n ?)?lu()?n ?)?LU?)? A?)?en? $?6? ?n ?=A = LU . 3?d?lu ?d? A? ? L

11、U?)"X)?+) .h? ?m?;? . . .% ? LU?)"01.0000003.00004.5000>>L,U=lu(A)L=0.14290.57141.00007.0000001.00000.500008.00000.85710U=3. ?)?qr()? ?)?QR?)? A?)? Q?n R ?=A = QR. qr? ?QR?) ?"? $?6?>>A=123;456;789;101112;)?+) .% QR?)h? ?m?;? . . .>>Q,R=qr(A)-0.8331-0.4512-0.06940.31

12、24Q=-0.0776-0.3105-0.5433-0.77620.5444-0.7709-0.09130.31780.06050.3251-0.83170.4461R=-12.8841000-14.5916-1.041300-16.2992-2.08260.000004. ?)?svd()? A?)? U !? S? V ?=? $?6?)?+) .A = USV T .h? ?m?;? . . .% ? ? ? ? ?>>)"U,S,V=svd(A)U=0.14090.34390.54700.75010.82470.42630.0278-0.37060.5477-0.

13、7361-0.17090.35930.00780.3977-0.81900.4134? $?6?S=25.462400?)?+) .0000.50450.57450.64451.290700-0.7608-0.05710.646500.000000.4082-0.81650.4082h? ?m?;? . . .V=5. A ?)?eig()? A A ?A A ?">>>>A=1D2=3;456;789;? $?6?Q,eig(A)?)?+) .h? ?m?;? . . .Q=0.23200.52530.818716.1168000.78580.0868-0.

14、61230-1.116800.4082-0.81650.4082000.0000D=?D ? ?dii? A 1i?A ?Q 1i ?A1i?A ? A ?"1.7.? ?1. ? ? ? u u sin cos? $?6?)?+) . ? ? m? ? tan abs sqrth? ?m?;? . . . exp log ?3 ?$? C?!?|? "XJgC?!?|? ?A ?C?!?|? "? $?2. ? k' ?(1) norm?"? ? 2 ?2?"X?6?)?+) .>> A = 1 2 3; 4 5 6; 7

15、 8 9;h? ?m?;? . . .>>norm(A)ans=16.8481(2) cond?"? ?"X>>cond(A)ans=3.7740e+016? $?6?(3) rank?"? ?"X?)?>>rank(A)?+) .h? ?m?;? . . .ans=2(4) zeors? ? " ) ? " ? ? " ? ? " X ) ? ?113 "? ?>>a=zeros(1,3)0a=00(5) ones?")? ?1 ? ?"

16、;X)?113 ?1 ? ? $?6?>>b=ones(1,3)?+) .b=111h? ?m?;? . . .(6) eye?")? ?"X)?3 × 3 ? >>I=eye(3)I=100010001? $?(7) size?"? ? ?"X>>size(A)?6?)?+) .ans=33h? ?m?;? . . .L? A?3 × 3 "(8) length?"? ?"X>>length(b)ans=3L?b?3? "22.1.?6?for

17、? $?6?for ?)?+) .for ?C?C?l,?m? ,?(?end?for ?h? ?m?;? . . .Xfor i=1: n?end% ?N? ?1?% ? dlform?end(?i"Xfori=j1:5? $?6?for=1:5?)?a(i,j) endend=1/(i+j-1);?+) .h? ?m?;? . . .a=1.00000.50000.33330.25000.20000.50000.33330.25000.20000.16670.33330.25000.20000.16670.14290.25000.20000.16670.14290.12500.2

18、0000.16670.14290.12500.1111? $?6?)?2.2.while ?+) .h? ?m?;? . . .while ?while ?1?end? ?O?1000?S Fibonacci?fi=11;1;? $?6?whilef(i)+f(i+1)<1000)?+) .h? ?m?;? . . .f(i+2)=f(i)+f(i+1);iend=i+1;f=Columns13through12131125821345589144Columns13through9872.3.if ?break ?if ? ?k?eA? $?6? if)?+) .?h? ?m?;? .

19、. .end? if?1else?2end? $?6?1? if?)?1elseif?2?2else?3?+) .h? ?m?;? . . .end? $?6?)?+) .break?y3?L?a?=?(?"e? ?S? ? ?XJ?K?2?K?3 21?E?L?T?C?1?"h? ?m?;? . . .while1input(Entern=n,negativequits.);ifn<=0? $?6?break;end?)?+) .h? ?m?;? . . .whilen>1ifnrem(n,2)=0=n/2;elsen endendend=3*n+1;3?S?

20、rem?"33.1.? $?6?M? ?-?M?)?+) .3h? ?m?;? . . .? ?1"X?O?1000?S Fibonacci? ?-f=11;i=1;whilef(i)+f(i+1)<1000f(i+2) i=i+1;end=f(i)+f(i+1);? $?6? ?M?*?.m?X?fibon.m?)? 3J?e?fibon?K?g?1?+) .h? ?m?;? . . .? z?-?O?(J"Columns1through121311235821345589144Columns13through9873.2.?*?.m? ?-N? $?6?

21、)?+) .?function ?C?=?gC?%?h? ?m?;? . . .? ?O? ?"?IO ?stat.m"functionmean,stdev=stat(x)% ? ?"? ? $?6?% XJx?,KmeanL?x ?"?stdevL?x ? ?%)?+) .h? ?m?;? . . .% XJx? ,%KmeanL?x? ?"?stdevL?x? ? m,n=size(x);ifm=1m=n; endmean=sum(x)/m;stdev=sqrt(sum(x.2)/m-mean.2);3J?e? $?>>>

22、>x=1234;3456;?6?mean,std=stat(x)?+) .mean=h? ?m?;? . . .2.50004.5000std=1.11801.11803M?J?S ?3?help?-?w?M?u?1?A1? ?"3.3.? ? ?C? ? ?"X?1. ?m?m? ?-? $?6?)?+) .h? ?m?;? . . .= fopen(?, #Na.)fid#Na.kr ?.a V.2. '4?'4? ?-?w ? .r+ ? .fclose(fid)? $?3. ? ? ?-?6?)?+) .h? ?m?;? . . .fprint

23、f(fid,?)?a.k%d ?%e ?%s i?2:?2:?1%f%gn? $?6?X?)?x=0:.1:1;y=x;exp(x);?+) .h? ?m?;? . . .fid=fopen(exp.txt,w);fprintf(fid,%6.2ffclose(fid)%12.8fn,y); ? exp.txt ? ?eT?3?K)?#?eT?3?K#?CX ?"? $?6?4. ?)?+) .? ?-?fscanf(fid,?)Xh? ?m?;? . . .% ?i?G% ?5? ?SA=fscanf(fid,%s)fscanf(fid,%5d)? $?4?6?)?4.1.?1.

24、x?:? x?:? ?-?plot(x,y,s)?x?I?y?p?I?s?J?"?eL?+) .h? ?m?;? . . .?y?.P?:?-? $?6?)? J?d: ?m c r g b wko x+* s d v:-.-?+) .h? ?m?;? . . .?7?x? ?(?en J?d?: ?J?d? ?X?3?x?y = esin x2 ?"x0, 54x=0:0.05:5;plot(x,y)y=exp(-x/4).*sin(x.2);? $?6?)?+) .h? ?m?;? . . .2. ?bar? ? ? ? x ? ? ? k ? ? ? " X

25、 xyex233, 3? ?"=x=-3:0.2:3; bar(x,exp(-x.*x);? $?6?)?+) .h? ?m?;? . . .3. 4?I?/polar?x? ?I?/"Xx? =| sin 2t · cos 2t|3? 4?I?/"t = 0: 0.01: 2*pi;? $?6?polar(t,abs(sin(2*t).*cos(2*t);?)?+) .h? ?m?;? . . .4.2.n?1. ? $?6?)?+) .mesh? x? n? ?" Xx?zsin x sin y3?, × , ? ?"x

26、 = -pi:0.3:pi;y = -pi:0.3:pi;=h? ?m?;? . . .X,Y=meshgrid(x,y);Z=sin(X).*sin(Y);mesh(X,Y,Z)? $?6?)?+) .h? ?m?;? . . .? $?6?)?+) .2. L?surf? x? n? L?" Xx?zsin x sin y3?, × , ? L?"surf(X,Y,Z)h? ?m?;? . . .=? $?6?)?+) .h? ?m?;? . . .? $?6?)?+) .3. p? ?contour?x? p?"Xx?z =sin x sin y3

27、?, × , ? p?"contour(X,Y,Z,16)?16? p? ?"h? ?m?;? . . .? $?6?)?+) .h? ?m?;? . . .3. n?x = x(t)? $?6?plot3?x?y = y(t),t , ?)?+) .z = z(t)h? ?m?;? . . .x = cos t? n?"Xx?y = sin t ,t 0, 6 z = 0.1tn?"ty=0:0.03:6*pi;x = cos(t);sin(t);z=0.1*t;plot3(x,y,z)? $?6?)?+) .h? ?m?;? . . .5)

28、? $?5.1.?|? )?)?|? )?)?dsolve.?)?I?3dsolve L? 3 L? i 1D L?D2, D3 L?p ?D ?i1?C?gC?dX?5K?"?X?6?)?+) .h? ?m?;? . . .d2ydy+ 3= 2dxdx2?L?D2y+3*Dy=2. ?LeZf?)"? $?6?)?du?+) .5.1? ?)"= 1 + u th? ?m?;? . . .dt)?-dsolve(Du=1+u-t,t), (J?ans=u(t) = t + Cet.=t+exp(t)*C15.2 ?e ? A)"(2d ydy+ 4+

29、 12y = 0dx? $?dx2?6?y(0) = 0, y0(0) = 5?)?+) .)?-h? ?m?;? . . .y=dsolve(D2y+4*Dy+12*y=0,y(0)=0,Dy(0)=5,x),(J?y=5/4*2(1/2)*exp(-2*x)*sin(2*2(1/2)*x)52y(x) = ) e2x.sin(22 x45.3?e ?| A)"? $? dx?6?= 2x 3y + 3z?dt)?dy?+) .= 4x 5y + 3z= 4x 4y + 2zh? ?m?;? . . .dt dzdt)?-x,y,z=dsolve(Dx=2*x-3*y+3*z,Dy

30、=4*x-5*y+3*z, Dz=4*x-4*y+2*z,t)(J?x=exp(2*t)*C1+C2*exp(-t)-C2*exp(2*t)? $?+exp(2*t)*C3-C3*exp(-t)=-C1*exp(-2*t)+exp(2*t)*C1+C2*exp(-2*t)?6?y?)?+) .+C2*exp(-t)-C2*exp(2*t)+exp(2*t)*C3-C3*exp(-t)=-C1*exp(-2*t)+exp(2*t)*C1-C2*exp(2*t)+C2*exp(-2*t)+exp(2*t)*C3h? ?m?;? . . .z=x(t) = C e+ C2(et e2t) + C3(e2t et),2t1y(t) = C (e e2t) + C2(e2t+ et et),2t2t2t e ) + C3(e1 z(t) = C1(e2t e2t) + C2(e2t e2t