octave:2> odefun = @(t,y) [-2*y(2)*y(1);... > y(1)^2+y(3)^2-y(2)^2-1;... > -2*(y(2)+y(1))*y(3)]; octave:3> y0=[0.5;2;10]; octave:4> odefun(0,y0) ans = -2.0000 95.2500 -50.0000 octave:5> options.Theta=1; octave:6> options.jacobian=@(t,y) [-2*y(2),-2*y(1),0;... > 2*y(1),-2*y(2),2*y(3);... > -2*y(3),-2*y(3),-2*(y(2)+y(1))]; octave:7> octave:7> options.Jacobian=@(t,y) [-2*y(2),-2*y(1),0;... > 2*y(1),-2*y(2),2*y(3);... > -2*y(3),-2*y(3),-2*(y(2)+y(1))]; octave:8> tspan=linspace(0,15,301); octave:9> help thetametodo 'thetametodo' is a function from the file /home/accounts/personale/clrmrc90/aa1920/equazioni_differenziali/thetametodo.m [tout, yout] = thetametodo (odefun, tspan, y0, options) Solve the ODE y'(t) = odefun (t, y(t)), where odefun is ... tspan is ... y0 is ... tout is ... options.Theta is ... Additional help for built-in functions and operators is available in the online version of the manual. Use the command 'doc ' to search the manual index. Help and information about Octave is also available on the WWW at http://www.octave.org and via the help@octave.org mailing list. octave:10> [tout,yout]=thetametodo(odefun,tspan,y0,options); octave:11> tout tout = 0.00000 0.05000 0.10000 0.15000 0.20000 0.25000 0.30000 0.35000 0.40000 0.45000 0.50000 0.55000 0.60000 0.65000 0.70000 0.75000 0.80000 0.85000 0.90000 0.95000 1.00000 1.05000 1.10000 1.15000 1.20000 1.25000 1.30000 1.35000 1.40000 1.45000 1.50000 1.55000 1.60000 1.65000 1.70000 1.75000 1.80000 1.85000 1.90000 1.95000 2.00000 2.05000 2.10000 2.15000 2.20000 2.25000 2.30000 2.35000 2.40000 2.45000 2.50000 2.55000 2.60000 2.65000 2.70000 2.75000 2.80000 2.85000 2.90000 2.95000 3.00000 3.05000 3.10000 3.15000 3.20000 3.25000 3.30000 3.35000 3.40000 3.45000 3.50000 3.55000 3.60000 3.65000 3.70000 3.75000 3.80000 3.85000 3.90000 3.95000 4.00000 4.05000 4.10000 4.15000 4.20000 4.25000 4.30000 4.35000 4.40000 4.45000 4.50000 4.55000 4.60000 4.65000 4.70000 4.75000 4.80000 4.85000 4.90000 4.95000 5.00000 5.05000 5.10000 5.15000 5.20000 5.25000 5.30000 5.35000 5.40000 5.45000 5.50000 5.55000 5.60000 5.65000 5.70000 5.75000 5.80000 5.85000 5.90000 5.95000 6.00000 6.05000 6.10000 6.15000 6.20000 6.25000 6.30000 6.35000 6.40000 6.45000 6.50000 6.55000 6.60000 6.65000 6.70000 6.75000 6.80000 6.85000 6.90000 6.95000 7.00000 7.05000 7.10000 7.15000 7.20000 7.25000 7.30000 7.35000 7.40000 7.45000 7.50000 7.55000 7.60000 7.65000 7.70000 7.75000 7.80000 7.85000 7.90000 7.95000 8.00000 8.05000 8.10000 8.15000 8.20000 8.25000 8.30000 8.35000 8.40000 8.45000 8.50000 8.55000 8.60000 8.65000 8.70000 8.75000 8.80000 8.85000 8.90000 8.95000 9.00000 9.05000 9.10000 9.15000 9.20000 9.25000 9.30000 9.35000 9.40000 9.45000 9.50000 9.55000 9.60000 9.65000 9.70000 9.75000 9.80000 9.85000 9.90000 9.95000 10.00000 10.05000 10.10000 10.15000 10.20000 10.25000 10.30000 10.35000 10.40000 10.45000 10.50000 10.55000 10.60000 10.65000 10.70000 10.75000 10.80000 10.85000 10.90000 10.95000 11.00000 11.05000 11.10000 11.15000 11.20000 11.25000 11.30000 11.35000 11.40000 11.45000 11.50000 11.55000 11.60000 11.65000 11.70000 11.75000 11.80000 11.85000 11.90000 11.95000 12.00000 12.05000 12.10000 12.15000 12.20000 12.25000 12.30000 12.35000 12.40000 12.45000 12.50000 12.55000 12.60000 12.65000 12.70000 12.75000 12.80000 12.85000 12.90000 12.95000 13.00000 13.05000 13.10000 13.15000 13.20000 13.25000 13.30000 13.35000 13.40000 13.45000 13.50000 13.55000 13.60000 13.65000 13.70000 13.75000 13.80000 13.85000 13.90000 13.95000 14.00000 14.05000 14.10000 14.15000 14.20000 14.25000 14.30000 14.35000 14.40000 14.45000 14.50000 14.55000 14.60000 14.65000 14.70000 14.75000 14.80000 14.85000 14.90000 14.95000 15.00000 octave:12> size(yout) ans = 301 3 octave:13> E=(yout(:,1).^2+yout(:,2).^2+yout(:,3).^2+1)./(2*yout(:,1)); octave:14> size(E) ans = 301 1 octave:15> plot(tout,E,'*') octave:16> epsilon=1e-4; octave:17> x=randn(3,1); octave:18> v=randn(3,1); octave:19> (odefun(0,x+epsilon*v)-odefun(0,x))/epsilon ans = -5.2910 -4.5682 3.0568 octave:20> options.Jacobian(0,x)*v ans = -5.2906 -4.5684 3.0569 octave:21> y0=1 y0 = 1 octave:22> y1=1 y1 = 1 octave:23> y2=3*y1-2*y0 y2 = 1 octave:24> y0=y1 y0 = 1 octave:25> y1=y2 y1 = 1 octave:26> y2=3*y1-2*y0 y2 = 1 octave:27> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:28> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:29> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:30> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:31> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:32> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:33> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:34> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:35> y0=y1;y1=y2;y2=3*y1-2*y0 y2 = 1 octave:36> y0=pi y0 = 3.1416 octave:37> format long e octave:38> y1=pi y1 = 3.14159265358979e+00 octave:39> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:40> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:41> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:42> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:43> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:44> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:45> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:46> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:47> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:48> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:49> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:50> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:51> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:52> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:53> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:54> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:55> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:56> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:57> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:58> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:59> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:60> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:61> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:62> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:63> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:64> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:65> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:66> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:67> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:68> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:69> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:70> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:71> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:72> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:73> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:74> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:75> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:76> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:77> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:78> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:79> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:80> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:81> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:82> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:83> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:84> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:85> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:86> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:87> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:88> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:89> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:90> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:91> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:92> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:93> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:94> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:95> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:96> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:97> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:98> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:99> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:100> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:101> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:102> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:103> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:104> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:105> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:106> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:107> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:108> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:109> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:110> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:111> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:112> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:113> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:114> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:115> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:116> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:117> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:118> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:119> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:120> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:121> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:122> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:123> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:124> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:125> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:126> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:127> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:128> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:129> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:130> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:131> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:132> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:133> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:134> 1+(eps/2+eps/2)>1 ans = 1 octave:135> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:136> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:137> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:138> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:139> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:140> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:141> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:142> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:143> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:144> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:145> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:146> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:147> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:148> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:149> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:150> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:151> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:152> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:153> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:154> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:155> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.14159265358979e+00 octave:156> y0=1/3 y0 = 3.33333333333333e-01 octave:157> y1=1/3 y1 = 3.33333333333333e-01 octave:158> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333333e-01 octave:159> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333333e-01 octave:160> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333333e-01 octave:161> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333333e-01 octave:162> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333333e-01 octave:163> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333332e-01 octave:164> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333330e-01 octave:165> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333326e-01 octave:166> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333319e-01 octave:167> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333305e-01 octave:168> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333277e-01 octave:169> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333220e-01 octave:170> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333333106e-01 octave:171> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333332879e-01 octave:172> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333332424e-01 octave:173> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333331514e-01 octave:174> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333329696e-01 octave:175> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333326058e-01 octave:176> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333318782e-01 octave:177> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333304230e-01 octave:178> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333275126e-01 octave:179> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333216918e-01 octave:180> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333333100503e-01 octave:181> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333332867672e-01 octave:182> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333332402011e-01 octave:183> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333331470688e-01 octave:184> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333329608043e-01 octave:185> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333325882753e-01 octave:186> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333318432172e-01 octave:187> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333303531011e-01 octave:188> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333273728689e-01 octave:189> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333214124044e-01 octave:190> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33333094914754e-01 octave:191> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33332856496175e-01 octave:192> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33332379659017e-01 octave:193> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33331425984701e-01 octave:194> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33329518636068e-01 octave:195> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33325703938802e-01 octave:196> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33318074544271e-01 octave:197> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33302815755208e-01 octave:198> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33272298177083e-01 octave:199> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33211263020833e-01 octave:200> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.33089192708333e-01 octave:201> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.32845052083333e-01 octave:202> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.32356770833333e-01 octave:203> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.31380208333333e-01 octave:204> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.29427083333333e-01 octave:205> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.25520833333333e-01 octave:206> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.17708333333333e-01 octave:207> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 3.02083333333333e-01 octave:208> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 2.70833333333333e-01 octave:209> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 2.08333333333333e-01 octave:210> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = 8.33333333333335e-02 octave:211> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -1.66666666666667e-01 octave:212> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -6.66666666666667e-01 octave:213> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -1.66666666666667e+00 octave:214> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -3.66666666666667e+00 octave:215> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -7.66666666666667e+00 octave:216> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -1.56666666666667e+01 octave:217> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -3.16666666666667e+01 octave:218> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -6.36666666666667e+01 octave:219> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -1.27666666666667e+02 octave:220> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -2.55666666666667e+02 octave:221> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -5.11666666666667e+02 octave:222> y2=3*y1-2*y0,y0=y1;y1=y2; y2 = -1.02366666666667e+03 octave:223> help rk2 'rk2' is a function from the file /home/accounts/personale/clrmrc90/aa1920/equazioni_differenziali/rk2.m Metodo di Eulero modificato function [tout,yout] = rk2(odefun,tspan,y0,options) tspan = [t0,t0+tstar] Additional help for built-in functions and operators is available in the online version of the manual. Use the command 'doc ' to search the manual index. Help and information about Octave is also available on the WWW at http://www.octave.org and via the help@octave.org mailing list. octave:224> odefun odefun = @(t, y) [-2 * y(2) * y(1); y(1) ^ 2 + y(3) ^ 2 - y(2) ^ 2 - 1; -2 * (y(2) + y(1)) * y(3)] octave:225> y0=[0.5;2;10]; octave:226> [tout,yout]=rk2(odefun,[0,15],y0); octave:227> E=(yout(:,1).^2+yout(:,2).^2+yout(:,3).^2+1)./(2*yout(:,1)); octave:228> plot(tout,E,'*') octave:229> octave:229> quit