matlab实验9答案详解.doc

实验九 数值微积分与方程数值求解一、实验目的1. 掌握求数值导数和数值积分的方法2. 掌握代数方程数值求解方法3. 掌握常微分方程数值求解方法二、实验内容1.程序代码x=1;i=1;f=inline(det(x x2 x3;1 2*x 3*x2;0 2 6*x);while x0 %非齐次方程组 if rank(A)=rank(A,b) if rank(A)=n disp(有唯一解x); x=Ab; else disp(有无穷个解，特解x，基础解系y); x=Ab; y=null(A,r); end else disp(无解); x= ; endelse %齐次方程组 disp(有零解x); x=zeros(n,1); if rank(A) In line_solution at 11x = -2/11 10/11 0 0 y = 1/11 -9/11 -5/11 1/11 1 0 0 1 说明，其中为任意常数。5. （1）程序代码function g=f(x)g=3*x+sin(x)-exp(x);命令fzero(f,1.5)运行结果ans =1289/682 （2） 程序代码function F=fun(X)x=X(1); y=X(2); z=X(3); F(1)=sin(x)+y2+log(z)-7; F(2)=3*x+2-z3+1; F(3)=x+y+z-5; 命令 X=fsolve(myfun,1,1,1,optimset(Display,off)运行结果X = 909/1073 1735/728 1106/6256. 程序代码function f=g(u)x=u(1); y=u(2); f=2*x.3+4*x.*y3-10*x.*y+y.2;命令format longf=inline(x3+cos(x)+x*log(x)/exp(x);x,fmin1=fminbnd(f,0,1)U,fmin2=fminsearch(g,0,0)运行结果x = 0.52228834066617fmin1 = 0.39736346499846U = 1.00157013531668 0.83348828276574fmin2 = -3.324088491954237. 程序代码function xdot= sys(x,y)xdot=y(2);(5*y(2)-y(1)/x; 命令x0=1.0e-9;xf=20;x,y=ode45(sys,x0,xf,0 0);x,y 运行结果ans = 0.00000000100000 0 0 0.50000000097500 0 0 1.00000000095000 0 0 1.50000000092500 0 0 2.00000000090000 0 0 2.50000000087500 0 0 3.00000000085000 0 0 3.50000000082500 0 0 4.00000000080000 0 0 4.50000000077500 0 0 5.00000000075000 0 0 5.50000000072500 0 0 6.00000000070000 0 0 6.50000000067500 0 0 7.00000000065000 0 0 7.50000000062500 0 0 8.00000000060000 0 0 8.50000000057500 0 0 9.00000000055000 0 0 9.50000000052500 0 0 10.00000000050000 0 0 10.50000000047500 0 0 11.00000000045000 0 0 11.50000000042500 0 0 12.00000000040000 0 0 12.50000000037500 0 0 13.00000000035000 0 0 13.50000000032500 0 0 14.00000000030000 0 0 14.50000000027500 0 0 15.00000000025000 0 0 15.50000000022500 0 0 16.00000000020000 0 0 16.50000000017500 0 0 17.00000000015000 0 0 17.50000000012500 0 0 18.00000000010000 0 0 18.50000000007500 0 0 19.00000000005000 0 0 19.50000000002500 0 0 20.00000000000000 0 08. 程序代码function xdot=sys(x,y)xdot=y(2)*y(3);-y(1)*y(3);-0.51*y(1)*y(2); 命令t0=0;tf=8;x,y=ode23(sys,t0,tf,0,1,1)plot(x,y) 运行结果x = 0 0.00008000000000 0.00048000000000 0.00248000000000 0.01248000000000 0.06248000000000 0.16316648087424 0.30334485269993 0.48294833967376 0.71624621246687 0.98493918956028 1.26102936892963 1.56781298101399 1.95504167569316 2.32873602272301 2.70243036975286 3.01525347944023 3.29207876536554 3.48893042863855 3.64518246216301 3.75378914221393 3.86239582226485 3.99407711326142 4.16449735950485 4.38346049900962 4.65366905664880 4.92651991704096 5.22446717648585 5.58606842661006 6.03015135143159 6.34283742936188 6.65552350729217 6.93710062286368 7.15413202687009 7.32381272703587 7.45016281067983 7.57651289432379 7.70417366782409 7.87056646578704 8.00000000000000y = 0 1.00000000000000 1.00000000000000 0.00007999999987 0.99999999680000 0.99999999836800 0.00047999997217 0.99999988480001 0.99999994124800 0.00247999616133 0.99999692480378 0.99999843165111 0.01247951083310 0.99992212724247 0.99996028565141 0.06241866084392 0.99804966035035 0.99900580258575 0.16207993349816 0.98677077677398 0.99327512367842 0.29648257808915 0.95500730947069 0.97731281155849 0.45626180734456 0.88975128335880 0.94538299205165 0.63501989875064 0.77223119924652 0.89115403037424 0.79436723160944 0.60687889820281 0.82334517154014 0.90691719876177 0.42032320550870 0.76171275015507 0.97795854279956 0.20660136122494 0.71547587549052 0.99746157200322 -0.06435382609456 0.70161030203131 0.94495832536325 -0.32577476314727 0.73774616015903 0.81273846068860 -0.58169326760580 0.81411075040892 0.63026715596716 -0.77548304089530 0.89273549643704 0.41296879043399 -0.90977435655485 0.95521547207918 0.23239805938823 -0.97163632839229 0.98579902579032 0.07945302792639 -0.99584330144411 0.99804308400598 -0.02887649481307 -0.99858177100716 0.99943757138815 -0.13669190064326 -0.98959458697952 0.99486819989785 -0.26403522164101 -0.96344776762242 0.98169211459246 -0.41874355211670 -0.90692284918313 0.95383599928875 -0.59348683151203 -0.80338578881180 0.90526486000873 -0.76435277266500 -0.64273606310776 0.83729511626613 -0.88586008956222 -0.46089846565828 0.77379347428854 -0.96564631710271 -0.25417823959890 0.72346612824858 -0.99852052429922 -0.00136968722324 0.70033669091483 -0.94946582197601 0.30917649189383 0.73430745677015 -0.84954447765781 0.52467093998805 0.79427803150432 -0.68575520763787 0.72561102860141 0.87124443849711 -0.48022003592803 0.87511116358204 0.93870074301866 -0.28880511014799 0.95541991873655 0.97782577819325 -0.12536463543148 0.99016523362993 0.99529929352736 0.0001575432219