octave:2> options.InitialStep=0.05 options = scalar structure containing the fields: InitialStep = 0.050000 octave:3> options.AbsTol=1e-6; octave:4> options options = scalar structure containing the fields: InitialStep = 0.050000 AbsTol = 1.0000e-06 octave:5> options.name='Marco' options = scalar structure containing the fields: InitialStep = 0.050000 AbsTol = 1.0000e-06 name = Marco octave:6> f=@(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:7> y0=[0.5;2;10]; octave:8> tspan=[0,15]; octave:9> [tout,yout]=rk2(f,tspan,y0); octave:10> 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:11> yout yout = 5.0000e-01 2.0000e+00 1.0000e+01 3.0284e-01 4.8285e+00 5.7727e+00 1.8669e-01 4.4238e+00 3.5042e+00 1.2537e-01 3.8491e+00 2.3278e+00 8.9030e-02 3.3293e+00 1.6394e+00 6.6065e-02 2.8931e+00 1.2087e+00 5.0833e-02 2.5330e+00 9.2528e-01 4.0315e-02 2.2350e+00 7.3082e-01 3.2801e-02 1.9858e+00 5.9258e-01 2.7273e-02 1.7750e+00 4.9133e-01 2.3104e-02 1.5944e+00 4.1523e-01 1.9893e-02 1.4377e+00 3.5678e-01 1.7375e-02 1.3001e+00 3.1105e-01 1.5368e-02 1.1780e+00 2.7469e-01 1.3748e-02 1.0686e+00 2.4538e-01 1.2425e-02 9.6966e-01 2.2148e-01 1.1334e-02 8.7935e-01 2.0181e-01 1.0429e-02 7.9626e-01 1.8548e-01 9.6712e-03 7.1925e-01 1.7184e-01 9.0353e-03 6.4737e-01 1.6039e-01 8.4998e-03 5.7982e-01 1.5075e-01 8.0483e-03 5.1593e-01 1.4263e-01 7.6682e-03 4.5515e-01 1.3579e-01 7.3494e-03 3.9698e-01 1.3004e-01 7.0840e-03 3.4101e-01 1.2526e-01 6.8657e-03 2.8685e-01 1.2131e-01 6.6896e-03 2.3418e-01 1.1812e-01 6.5520e-03 1.8270e-01 1.1562e-01 6.4500e-03 1.3212e-01 1.1374e-01 6.3814e-03 8.2191e-02 1.1246e-01 6.3450e-03 3.2655e-02 1.1175e-01 6.3399e-03 -1.6724e-02 1.1159e-01 6.3662e-03 -6.6184e-02 1.1198e-01 6.4243e-03 -1.1597e-01 1.1293e-01 6.5154e-03 -1.6631e-01 1.1446e-01 6.6413e-03 -2.1748e-01 1.1659e-01 6.8047e-03 -2.6975e-01 1.1938e-01 7.0090e-03 -3.2340e-01 1.2288e-01 7.2587e-03 -3.7876e-01 1.2717e-01 7.5597e-03 -4.3620e-01 1.3234e-01 7.9193e-03 -4.9612e-01 1.3853e-01 8.3468e-03 -5.5899e-01 1.4589e-01 8.8541e-03 -6.2534e-01 1.5463e-01 9.4563e-03 -6.9581e-01 1.6499e-01 1.0173e-02 -7.7116e-01 1.7732e-01 1.1029e-02 -8.5229e-01 1.9204e-01 1.2057e-02 -9.4029e-01 2.0971e-01 1.3303e-02 -1.0365e+00 2.3108e-01 1.4824e-02 -1.1426e+00 2.5714e-01 1.6702e-02 -1.2608e+00 2.8928e-01 1.9051e-02 -1.3936e+00 3.2939e-01 2.2036e-02 -1.5446e+00 3.8023e-01 2.5895e-02 -1.7183e+00 4.4577e-01 3.0990e-02 -1.9208e+00 5.3203e-01 3.7889e-02 -2.1600e+00 6.4832e-01 4.7507e-02 -2.4467e+00 8.0961e-01 6.1396e-02 -2.7947e+00 1.0410e+00 8.2304e-02 -3.2208e+00 1.3862e+00 1.1534e-01 -3.7393e+00 1.9253e+00 1.7038e-01 -4.3381e+00 2.8086e+00 2.6650e-01 -4.8846e+00 4.3115e+00 4.3360e-01 -4.7907e+00 6.8100e+00 6.6070e-01 -2.2798e+00 9.8685e+00 6.5990e-01 3.3870e+00 9.0718e+00 3.7796e-01 4.6473e+00 4.9532e+00 2.4162e-01 4.1851e+00 3.1028e+00 1.6588e-01 3.6429e+00 2.0988e+00 1.1979e-01 3.1612e+00 1.4986e+00 9.0110e-02 2.7572e+00 1.1173e+00 7.0117e-02 2.4222e+00 8.6324e-01 5.6132e-02 2.1435e+00 6.8710e-01 4.6031e-02 1.9092e+00 5.6078e-01 3.8532e-02 1.7099e+00 4.6755e-01 3.2833e-02 1.5383e+00 3.9704e-01 2.8414e-02 1.3887e+00 3.4259e-01 2.4928e-02 1.2569e+00 2.9978e-01 2.2137e-02 1.1395e+00 2.6560e-01 1.9874e-02 1.0339e+00 2.3797e-01 1.8021e-02 9.3811e-01 2.1537e-01 1.6488e-02 8.5042e-01 1.9672e-01 1.5212e-02 7.6953e-01 1.8121e-01 1.4143e-02 6.9437e-01 1.6823e-01 1.3245e-02 6.2405e-01 1.5733e-01 1.2488e-02 5.5782e-01 1.4815e-01 1.1850e-02 4.9505e-01 1.4041e-01 1.1313e-02 4.3521e-01 1.3390e-01 1.0864e-02 3.7783e-01 1.2844e-01 1.0491e-02 3.2252e-01 1.2390e-01 1.0187e-02 2.6890e-01 1.2018e-01 9.9429e-03 2.1667e-01 1.1719e-01 9.7552e-03 1.6553e-01 1.1486e-01 9.6196e-03 1.1520e-01 1.1316e-01 9.5333e-03 6.5427e-02 1.1203e-01 9.4947e-03 1.5972e-02 1.1147e-01 9.5030e-03 -3.3408e-02 1.1147e-01 9.5583e-03 -8.2950e-02 1.1201e-01 9.6618e-03 -1.3289e-01 1.1311e-01 9.8154e-03 -1.8349e-01 1.1480e-01 1.0022e-02 -2.3500e-01 1.1711e-01 1.0287e-02 -2.8770e-01 1.2008e-01 1.0615e-02 -3.4190e-01 1.2378e-01 1.1014e-02 -3.9792e-01 1.2829e-01 1.1493e-02 -4.5615e-01 1.3372e-01 1.2064e-02 -5.1702e-01 1.4020e-01 1.2743e-02 -5.8100e-01 1.4790e-01 1.3548e-02 -6.4868e-01 1.5704e-01 1.4504e-02 -7.2072e-01 1.6789e-01 1.5643e-02 -7.9793e-01 1.8081e-01 1.7006e-02 -8.8127e-01 1.9624e-01 1.8648e-02 -9.7191e-01 2.1481e-01 2.0641e-02 -1.0713e+00 2.3731e-01 2.3085e-02 -1.1813e+00 2.6483e-01 2.6115e-02 -1.3041e+00 2.9887e-01 2.9924e-02 -1.4428e+00 3.4153e-01 3.4791e-02 -1.6011e+00 3.9583e-01 4.1128e-02 -1.7841e+00 4.6620e-01 4.9564e-02 -1.9985e+00 5.5937e-01 6.1097e-02 -2.2533e+00 6.8589e-01 7.7367e-02 -2.5605e+00 8.6287e-01 1.0120e-01 -2.9359e+00 1.1193e+00 1.3769e-01 -3.3980e+00 1.5063e+00 1.9656e-01 -3.9611e+00 2.1183e+00 2.9701e-01 -4.6011e+00 3.1326e+00 4.7631e-01 -5.1242e+00 4.8619e+00 7.8798e-01 -4.7179e+00 7.6244e+00 1.1610e+00 -1.2930e+00 1.0231e+01 1.0015e+00 3.9526e+00 7.6287e+00 5.9835e-01 4.3232e+00 4.2882e+00 3.9670e-01 3.8825e+00 2.7465e+00 2.7927e-01 3.3960e+00 1.8845e+00 2.0569e-01 2.9635e+00 1.3607e+00 1.5723e-01 2.5980e+00 1.0239e+00 1.2397e-01 2.2924e+00 7.9719e-01 1.0034e-01 2.0359e+00 6.3865e-01 8.3060e-02 1.8187e+00 5.2412e-01 7.0088e-02 1.6327e+00 4.3905e-01 6.0137e-02 1.4714e+00 3.7437e-01 5.2360e-02 1.3301e+00 3.2419e-01 4.6184e-02 1.2050e+00 2.8458e-01 4.1211e-02 1.0930e+00 2.5286e-01 3.7160e-02 9.9185e-01 2.2713e-01 3.3828e-02 8.9972e-01 2.0604e-01 3.1064e-02 8.1510e-01 1.8860e-01 2.8756e-02 7.3679e-01 1.7407e-01 2.6820e-02 6.6380e-01 1.6191e-01 2.5191e-02 5.9531e-01 1.5168e-01 2.3817e-02 5.3062e-01 1.4306e-01 2.2660e-02 4.6916e-01 1.3579e-01 2.1688e-02 4.1042e-01 1.2968e-01 2.0877e-02 3.5397e-01 1.2457e-01 2.0208e-02 2.9941e-01 1.2033e-01 1.9666e-02 2.4642e-01 1.1687e-01 1.9238e-02 1.9468e-01 1.1411e-01 1.8916e-02 1.4390e-01 1.1198e-01 1.8693e-02 9.3834e-02 1.1046e-01 1.8565e-02 4.4217e-02 1.0949e-01 1.8529e-02 -5.1894e-03 1.0908e-01 1.8584e-02 -5.4623e-02 1.0920e-01 1.8732e-02 -1.0432e-01 1.0987e-01 1.8975e-02 -1.5453e-01 1.1109e-01 1.9319e-02 -2.0550e-01 1.1288e-01 1.9771e-02 -2.5751e-01 1.1530e-01 2.0339e-02 -3.1084e-01 1.1837e-01 2.1037e-02 -3.6580e-01 1.2218e-01 2.1880e-02 -4.2276e-01 1.2681e-01 2.2890e-02 -4.8211e-01 1.3237e-01 2.4091e-02 -5.4429e-01 1.3899e-01 2.5517e-02 -6.0985e-01 1.4685e-01 2.7209e-02 -6.7938e-01 1.5618e-01 2.9222e-02 -7.5362e-01 1.6726e-01 3.1624e-02 -8.3344e-01 1.8047e-01 3.4506e-02 -9.1991e-01 1.9627e-01 3.7989e-02 -1.0143e+00 2.1531e-01 4.2236e-02 -1.1183e+00 2.3844e-01 4.7467e-02 -1.2338e+00 2.6679e-01 5.3994e-02 -1.3635e+00 3.0197e-01 6.2256e-02 -1.5108e+00 3.4620e-01 7.2902e-02 -1.6801e+00 4.0274e-01 8.6901e-02 -1.8772e+00 4.7638e-01 1.0576e-01 -2.1102e+00 5.7445e-01 1.3193e-01 -2.3900e+00 7.0851e-01 1.6952e-01 -2.7316e+00 8.9752e-01 2.2582e-01 -3.1555e+00 1.1739e+00 3.1455e-01 -3.6873e+00 1.5954e+00 4.6305e-01 -4.3511e+00 2.2692e+00 7.2889e-01 -5.1296e+00 3.3944e+00 1.2336e+00 -5.7987e+00 5.2974e+00 2.1764e+00 -5.3605e+00 8.1169e+00 3.3737e+00 -1.5441e+00 9.6022e+00 3.0245e+00 2.8253e+00 5.5936e+00 2.0864e+00 3.2435e+00 3.1364e+00 1.5078e+00 3.0630e+00 1.9727e+00 1.1301e+00 2.7730e+00 1.3283e+00 8.7395e-01 2.4812e+00 9.4286e-01 6.9454e-01 2.2167e+00 6.9889e-01 5.6528e-01 1.9845e+00 5.3702e-01 4.6974e-01 1.7824e+00 4.2525e-01 3.9751e-01 1.6062e+00 3.4540e-01 3.4181e-01 1.4517e+00 2.8669e-01 2.9810e-01 1.3150e+00 2.4242e-01 2.6327e-01 1.1932e+00 2.0835e-01 2.3516e-01 1.0837e+00 1.8163e-01 2.1222e-01 9.8438e-01 1.6036e-01 1.9331e-01 8.9366e-01 1.4319e-01 1.7761e-01 8.1015e-01 1.2918e-01 1.6449e-01 7.3271e-01 1.1763e-01 1.5347e-01 6.6043e-01 1.0804e-01 1.4419e-01 5.9251e-01 1.0002e-01 1.3636e-01 5.2830e-01 9.3281e-02 1.2977e-01 4.6724e-01 8.7602e-02 1.2422e-01 4.0883e-01 8.2807e-02 1.1960e-01 3.5267e-01 7.8762e-02 1.1578e-01 2.9837e-01 7.5359e-02 1.1268e-01 2.4561e-01 7.2512e-02 1.1024e-01 1.9407e-01 7.0156e-02 1.0840e-01 1.4348e-01 6.8238e-02 1.0712e-01 9.3589e-02 6.6715e-02 1.0639e-01 4.4139e-02 6.5557e-02 1.0618e-01 -5.1047e-03 6.4739e-02 1.0650e-01 -5.4377e-02 6.4246e-02 1.0734e-01 -1.0391e-01 6.4069e-02 1.0873e-01 -1.5396e-01 6.4203e-02 1.1069e-01 -2.0475e-01 6.4650e-02 1.1327e-01 -2.5657e-01 6.5420e-02 1.1652e-01 -3.0970e-01 6.6528e-02 1.2050e-01 -3.6444e-01 6.7994e-02 1.2531e-01 -4.2114e-01 6.9850e-02 1.3107e-01 -4.8020e-01 7.2133e-02 1.3792e-01 -5.4205e-01 7.4894e-02 1.4605e-01 -6.0722e-01 7.8196e-02 1.5569e-01 -6.7630e-01 8.2118e-02 1.6715e-01 -7.4999e-01 8.6760e-02 1.8082e-01 -8.2915e-01 9.2249e-02 1.9721e-01 -9.1479e-01 9.8744e-02 2.1700e-01 -1.0082e+00 1.0645e-01 2.4109e-01 -1.1108e+00 1.1563e-01 2.7074e-01 -1.2247e+00 1.2661e-01 3.0765e-01 -1.3523e+00 1.3984e-01 3.5430e-01 -1.4966e+00 1.5591e-01 4.1424e-01 -1.6619e+00 1.7557e-01 4.9279e-01 -1.8534e+00 1.9986e-01 5.9817e-01 -2.0781e+00 2.3014e-01 7.4350e-01 -2.3454e+00 2.6822e-01 9.5054e-01 -2.6673e+00 3.1636e-01 1.2570e+00 -3.0581e+00 3.7709e-01 1.7315e+00 -3.5306e+00 4.5208e-01 2.5030e+00 -4.0780e+00 5.3831e-01 3.8153e+00 -4.6054e+00 6.1622e-01 6.0624e+00 -4.6792e+00 6.2220e-01 9.2964e+00 -2.8488e+00 4.3932e-01 1.0264e+01 2.7039e+00 1.5028e-01 5.7101e+00 5.2776e+00 7.6271e-02 3.4523e+00 4.6684e+00 4.3363e-02 2.2887e+00 4.0021e+00 2.5223e-02 1.6100e+00 3.4324e+00 1.5648e-02 1.1862e+00 2.9664e+00 1.0368e-02 9.0769e-01 2.5875e+00 7.2736e-03 7.1678e-01 2.2770e+00 5.3492e-03 5.8116e-01 2.0192e+00 4.0891e-03 4.8185e-01 1.8022e+00 3.2271e-03 4.0724e-01 1.6170e+00 2.6153e-03 3.4994e-01 1.4568e+00 2.1675e-03 3.0511e-01 1.3166e+00 1.8310e-03 2.6946e-01 1.1925e+00 1.5727e-03 2.4073e-01 1.0814e+00 1.3705e-03 2.1731e-01 9.8112e-01 1.2097e-03 1.9802e-01 8.8971e-01 1.0800e-03 1.8202e-01 8.0572e-01 9.7432e-04 1.6865e-01 7.2796e-01 8.8726e-04 1.5743e-01 6.5545e-01 8.1497e-04 1.4798e-01 5.8737e-01 7.5457e-04 1.4002e-01 5.2304e-01 7.0384e-04 1.3332e-01 4.6188e-01 6.6110e-04 1.2769e-01 4.0340e-01 6.2504e-04 1.2300e-01 3.4716e-01 5.9462e-04 1.1914e-01 2.9278e-01 5.6905e-04 1.1602e-01 2.3993e-01 5.4769e-04 1.1357e-01 1.8830e-01 5.3002e-04 1.1174e-01 1.3761e-01 5.1565e-04 1.1049e-01 8.7597e-02 5.0427e-04 1.0980e-01 3.8005e-02 4.9565e-04 1.0965e-01 -1.1403e-02 4.8960e-04 1.1005e-01 -6.0866e-02 4.8602e-04 1.1099e-01 -1.1062e-01 4.8482e-04 1.1251e-01 -1.6092e-01 4.8598e-04 1.1462e-01 -2.1201e-01 4.8953e-04 1.1737e-01 -2.6417e-01 4.9553e-04 1.2083e-01 -3.1768e-01 5.0410e-04 1.2506e-01 -3.7288e-01 5.1541e-04 1.3017e-01 -4.3010e-01 5.2968e-04 1.3628e-01 -4.8977e-01 5.4722e-04 1.4354e-01 -5.5233e-01 5.6842e-04 1.5216e-01 -6.1832e-01 5.9377e-04 1.6240e-01 -6.8836e-01 6.2387e-04 1.7457e-01 -7.6320e-01 6.5951e-04 1.8910e-01 -8.4372e-01 7.0165e-04 2.0656e-01 -9.3099e-01 7.5154e-04 2.2767e-01 -1.0263e+00 8.1076e-04 2.5343e-01 -1.1314e+00 8.8134e-04 2.8521e-01 -1.2482e+00 9.6589e-04 3.2491e-01 -1.3795e+00 1.0679e-03 octave:12> E=(yout(:,1).^2+yout(:,2).^2+yout(:,3).^2+1)./(2*yout(:,1)); octave:13> plot(tout,E,'*') octave:14> options.InitialStep=0.025 options = scalar structure containing the fields: InitialStep = 0.025000 AbsTol = 1.0000e-06 name = Marco octave:15> [tout,yout]=rk2(f,tspan,y0,options); octave:16> E=(yout(:,1).^2+yout(:,2).^2+yout(:,3).^2+1)./(2*yout(:,1)); octave:17> plot(tout,E,'*') octave:18> [tout,yout]=rk2(f,tspan,y0); octave:19> yout yout = 5.0000e-01 2.0000e+00 1.0000e+01 3.0284e-01 4.8285e+00 5.7727e+00 1.8669e-01 4.4238e+00 3.5042e+00 1.2537e-01 3.8491e+00 2.3278e+00 8.9030e-02 3.3293e+00 1.6394e+00 6.6065e-02 2.8931e+00 1.2087e+00 5.0833e-02 2.5330e+00 9.2528e-01 4.0315e-02 2.2350e+00 7.3082e-01 3.2801e-02 1.9858e+00 5.9258e-01 2.7273e-02 1.7750e+00 4.9133e-01 2.3104e-02 1.5944e+00 4.1523e-01 1.9893e-02 1.4377e+00 3.5678e-01 1.7375e-02 1.3001e+00 3.1105e-01 1.5368e-02 1.1780e+00 2.7469e-01 1.3748e-02 1.0686e+00 2.4538e-01 1.2425e-02 9.6966e-01 2.2148e-01 1.1334e-02 8.7935e-01 2.0181e-01 1.0429e-02 7.9626e-01 1.8548e-01 9.6712e-03 7.1925e-01 1.7184e-01 9.0353e-03 6.4737e-01 1.6039e-01 8.4998e-03 5.7982e-01 1.5075e-01 8.0483e-03 5.1593e-01 1.4263e-01 7.6682e-03 4.5515e-01 1.3579e-01 7.3494e-03 3.9698e-01 1.3004e-01 7.0840e-03 3.4101e-01 1.2526e-01 6.8657e-03 2.8685e-01 1.2131e-01 6.6896e-03 2.3418e-01 1.1812e-01 6.5520e-03 1.8270e-01 1.1562e-01 6.4500e-03 1.3212e-01 1.1374e-01 6.3814e-03 8.2191e-02 1.1246e-01 6.3450e-03 3.2655e-02 1.1175e-01 6.3399e-03 -1.6724e-02 1.1159e-01 6.3662e-03 -6.6184e-02 1.1198e-01 6.4243e-03 -1.1597e-01 1.1293e-01 6.5154e-03 -1.6631e-01 1.1446e-01 6.6413e-03 -2.1748e-01 1.1659e-01 6.8047e-03 -2.6975e-01 1.1938e-01 7.0090e-03 -3.2340e-01 1.2288e-01 7.2587e-03 -3.7876e-01 1.2717e-01 7.5597e-03 -4.3620e-01 1.3234e-01 7.9193e-03 -4.9612e-01 1.3853e-01 8.3468e-03 -5.5899e-01 1.4589e-01 8.8541e-03 -6.2534e-01 1.5463e-01 9.4563e-03 -6.9581e-01 1.6499e-01 1.0173e-02 -7.7116e-01 1.7732e-01 1.1029e-02 -8.5229e-01 1.9204e-01 1.2057e-02 -9.4029e-01 2.0971e-01 1.3303e-02 -1.0365e+00 2.3108e-01 1.4824e-02 -1.1426e+00 2.5714e-01 1.6702e-02 -1.2608e+00 2.8928e-01 1.9051e-02 -1.3936e+00 3.2939e-01 2.2036e-02 -1.5446e+00 3.8023e-01 2.5895e-02 -1.7183e+00 4.4577e-01 3.0990e-02 -1.9208e+00 5.3203e-01 3.7889e-02 -2.1600e+00 6.4832e-01 4.7507e-02 -2.4467e+00 8.0961e-01 6.1396e-02 -2.7947e+00 1.0410e+00 8.2304e-02 -3.2208e+00 1.3862e+00 1.1534e-01 -3.7393e+00 1.9253e+00 1.7038e-01 -4.3381e+00 2.8086e+00 2.6650e-01 -4.8846e+00 4.3115e+00 4.3360e-01 -4.7907e+00 6.8100e+00 6.6070e-01 -2.2798e+00 9.8685e+00 6.5990e-01 3.3870e+00 9.0718e+00 3.7796e-01 4.6473e+00 4.9532e+00 2.4162e-01 4.1851e+00 3.1028e+00 1.6588e-01 3.6429e+00 2.0988e+00 1.1979e-01 3.1612e+00 1.4986e+00 9.0110e-02 2.7572e+00 1.1173e+00 7.0117e-02 2.4222e+00 8.6324e-01 5.6132e-02 2.1435e+00 6.8710e-01 4.6031e-02 1.9092e+00 5.6078e-01 3.8532e-02 1.7099e+00 4.6755e-01 3.2833e-02 1.5383e+00 3.9704e-01 2.8414e-02 1.3887e+00 3.4259e-01 2.4928e-02 1.2569e+00 2.9978e-01 2.2137e-02 1.1395e+00 2.6560e-01 1.9874e-02 1.0339e+00 2.3797e-01 1.8021e-02 9.3811e-01 2.1537e-01 1.6488e-02 8.5042e-01 1.9672e-01 1.5212e-02 7.6953e-01 1.8121e-01 1.4143e-02 6.9437e-01 1.6823e-01 1.3245e-02 6.2405e-01 1.5733e-01 1.2488e-02 5.5782e-01 1.4815e-01 1.1850e-02 4.9505e-01 1.4041e-01 1.1313e-02 4.3521e-01 1.3390e-01 1.0864e-02 3.7783e-01 1.2844e-01 1.0491e-02 3.2252e-01 1.2390e-01 1.0187e-02 2.6890e-01 1.2018e-01 9.9429e-03 2.1667e-01 1.1719e-01 9.7552e-03 1.6553e-01 1.1486e-01 9.6196e-03 1.1520e-01 1.1316e-01 9.5333e-03 6.5427e-02 1.1203e-01 9.4947e-03 1.5972e-02 1.1147e-01 9.5030e-03 -3.3408e-02 1.1147e-01 9.5583e-03 -8.2950e-02 1.1201e-01 9.6618e-03 -1.3289e-01 1.1311e-01 9.8154e-03 -1.8349e-01 1.1480e-01 1.0022e-02 -2.3500e-01 1.1711e-01 1.0287e-02 -2.8770e-01 1.2008e-01 1.0615e-02 -3.4190e-01 1.2378e-01 1.1014e-02 -3.9792e-01 1.2829e-01 1.1493e-02 -4.5615e-01 1.3372e-01 1.2064e-02 -5.1702e-01 1.4020e-01 1.2743e-02 -5.8100e-01 1.4790e-01 1.3548e-02 -6.4868e-01 1.5704e-01 1.4504e-02 -7.2072e-01 1.6789e-01 1.5643e-02 -7.9793e-01 1.8081e-01 1.7006e-02 -8.8127e-01 1.9624e-01 1.8648e-02 -9.7191e-01 2.1481e-01 2.0641e-02 -1.0713e+00 2.3731e-01 2.3085e-02 -1.1813e+00 2.6483e-01 2.6115e-02 -1.3041e+00 2.9887e-01 2.9924e-02 -1.4428e+00 3.4153e-01 3.4791e-02 -1.6011e+00 3.9583e-01 4.1128e-02 -1.7841e+00 4.6620e-01 4.9564e-02 -1.9985e+00 5.5937e-01 6.1097e-02 -2.2533e+00 6.8589e-01 7.7367e-02 -2.5605e+00 8.6287e-01 1.0120e-01 -2.9359e+00 1.1193e+00 1.3769e-01 -3.3980e+00 1.5063e+00 1.9656e-01 -3.9611e+00 2.1183e+00 2.9701e-01 -4.6011e+00 3.1326e+00 4.7631e-01 -5.1242e+00 4.8619e+00 7.8798e-01 -4.7179e+00 7.6244e+00 1.1610e+00 -1.2930e+00 1.0231e+01 1.0015e+00 3.9526e+00 7.6287e+00 5.9835e-01 4.3232e+00 4.2882e+00 3.9670e-01 3.8825e+00 2.7465e+00 2.7927e-01 3.3960e+00 1.8845e+00 2.0569e-01 2.9635e+00 1.3607e+00 1.5723e-01 2.5980e+00 1.0239e+00 1.2397e-01 2.2924e+00 7.9719e-01 1.0034e-01 2.0359e+00 6.3865e-01 8.3060e-02 1.8187e+00 5.2412e-01 7.0088e-02 1.6327e+00 4.3905e-01 6.0137e-02 1.4714e+00 3.7437e-01 5.2360e-02 1.3301e+00 3.2419e-01 4.6184e-02 1.2050e+00 2.8458e-01 4.1211e-02 1.0930e+00 2.5286e-01 3.7160e-02 9.9185e-01 2.2713e-01 3.3828e-02 8.9972e-01 2.0604e-01 3.1064e-02 8.1510e-01 1.8860e-01 2.8756e-02 7.3679e-01 1.7407e-01 2.6820e-02 6.6380e-01 1.6191e-01 2.5191e-02 5.9531e-01 1.5168e-01 2.3817e-02 5.3062e-01 1.4306e-01 2.2660e-02 4.6916e-01 1.3579e-01 2.1688e-02 4.1042e-01 1.2968e-01 2.0877e-02 3.5397e-01 1.2457e-01 2.0208e-02 2.9941e-01 1.2033e-01 1.9666e-02 2.4642e-01 1.1687e-01 1.9238e-02 1.9468e-01 1.1411e-01 1.8916e-02 1.4390e-01 1.1198e-01 1.8693e-02 9.3834e-02 1.1046e-01 1.8565e-02 4.4217e-02 1.0949e-01 1.8529e-02 -5.1894e-03 1.0908e-01 1.8584e-02 -5.4623e-02 1.0920e-01 1.8732e-02 -1.0432e-01 1.0987e-01 1.8975e-02 -1.5453e-01 1.1109e-01 1.9319e-02 -2.0550e-01 1.1288e-01 1.9771e-02 -2.5751e-01 1.1530e-01 2.0339e-02 -3.1084e-01 1.1837e-01 2.1037e-02 -3.6580e-01 1.2218e-01 2.1880e-02 -4.2276e-01 1.2681e-01 2.2890e-02 -4.8211e-01 1.3237e-01 2.4091e-02 -5.4429e-01 1.3899e-01 2.5517e-02 -6.0985e-01 1.4685e-01 2.7209e-02 -6.7938e-01 1.5618e-01 2.9222e-02 -7.5362e-01 1.6726e-01 3.1624e-02 -8.3344e-01 1.8047e-01 3.4506e-02 -9.1991e-01 1.9627e-01 3.7989e-02 -1.0143e+00 2.1531e-01 4.2236e-02 -1.1183e+00 2.3844e-01 4.7467e-02 -1.2338e+00 2.6679e-01 5.3994e-02 -1.3635e+00 3.0197e-01 6.2256e-02 -1.5108e+00 3.4620e-01 7.2902e-02 -1.6801e+00 4.0274e-01 8.6901e-02 -1.8772e+00 4.7638e-01 1.0576e-01 -2.1102e+00 5.7445e-01 1.3193e-01 -2.3900e+00 7.0851e-01 1.6952e-01 -2.7316e+00 8.9752e-01 2.2582e-01 -3.1555e+00 1.1739e+00 3.1455e-01 -3.6873e+00 1.5954e+00 4.6305e-01 -4.3511e+00 2.2692e+00 7.2889e-01 -5.1296e+00 3.3944e+00 1.2336e+00 -5.7987e+00 5.2974e+00 2.1764e+00 -5.3605e+00 8.1169e+00 3.3737e+00 -1.5441e+00 9.6022e+00 3.0245e+00 2.8253e+00 5.5936e+00 2.0864e+00 3.2435e+00 3.1364e+00 1.5078e+00 3.0630e+00 1.9727e+00 1.1301e+00 2.7730e+00 1.3283e+00 8.7395e-01 2.4812e+00 9.4286e-01 6.9454e-01 2.2167e+00 6.9889e-01 5.6528e-01 1.9845e+00 5.3702e-01 4.6974e-01 1.7824e+00 4.2525e-01 3.9751e-01 1.6062e+00 3.4540e-01 3.4181e-01 1.4517e+00 2.8669e-01 2.9810e-01 1.3150e+00 2.4242e-01 2.6327e-01 1.1932e+00 2.0835e-01 2.3516e-01 1.0837e+00 1.8163e-01 2.1222e-01 9.8438e-01 1.6036e-01 1.9331e-01 8.9366e-01 1.4319e-01 1.7761e-01 8.1015e-01 1.2918e-01 1.6449e-01 7.3271e-01 1.1763e-01 1.5347e-01 6.6043e-01 1.0804e-01 1.4419e-01 5.9251e-01 1.0002e-01 1.3636e-01 5.2830e-01 9.3281e-02 1.2977e-01 4.6724e-01 8.7602e-02 1.2422e-01 4.0883e-01 8.2807e-02 1.1960e-01 3.5267e-01 7.8762e-02 1.1578e-01 2.9837e-01 7.5359e-02 1.1268e-01 2.4561e-01 7.2512e-02 1.1024e-01 1.9407e-01 7.0156e-02 1.0840e-01 1.4348e-01 6.8238e-02 1.0712e-01 9.3589e-02 6.6715e-02 1.0639e-01 4.4139e-02 6.5557e-02 1.0618e-01 -5.1047e-03 6.4739e-02 1.0650e-01 -5.4377e-02 6.4246e-02 1.0734e-01 -1.0391e-01 6.4069e-02 1.0873e-01 -1.5396e-01 6.4203e-02 1.1069e-01 -2.0475e-01 6.4650e-02 1.1327e-01 -2.5657e-01 6.5420e-02 1.1652e-01 -3.0970e-01 6.6528e-02 1.2050e-01 -3.6444e-01 6.7994e-02 1.2531e-01 -4.2114e-01 6.9850e-02 1.3107e-01 -4.8020e-01 7.2133e-02 1.3792e-01 -5.4205e-01 7.4894e-02 1.4605e-01 -6.0722e-01 7.8196e-02 1.5569e-01 -6.7630e-01 8.2118e-02 1.6715e-01 -7.4999e-01 8.6760e-02 1.8082e-01 -8.2915e-01 9.2249e-02 1.9721e-01 -9.1479e-01 9.8744e-02 2.1700e-01 -1.0082e+00 1.0645e-01 2.4109e-01 -1.1108e+00 1.1563e-01 2.7074e-01 -1.2247e+00 1.2661e-01 3.0765e-01 -1.3523e+00 1.3984e-01 3.5430e-01 -1.4966e+00 1.5591e-01 4.1424e-01 -1.6619e+00 1.7557e-01 4.9279e-01 -1.8534e+00 1.9986e-01 5.9817e-01 -2.0781e+00 2.3014e-01 7.4350e-01 -2.3454e+00 2.6822e-01 9.5054e-01 -2.6673e+00 3.1636e-01 1.2570e+00 -3.0581e+00 3.7709e-01 1.7315e+00 -3.5306e+00 4.5208e-01 2.5030e+00 -4.0780e+00 5.3831e-01 3.8153e+00 -4.6054e+00 6.1622e-01 6.0624e+00 -4.6792e+00 6.2220e-01 9.2964e+00 -2.8488e+00 4.3932e-01 1.0264e+01 2.7039e+00 1.5028e-01 5.7101e+00 5.2776e+00 7.6271e-02 3.4523e+00 4.6684e+00 4.3363e-02 2.2887e+00 4.0021e+00 2.5223e-02 1.6100e+00 3.4324e+00 1.5648e-02 1.1862e+00 2.9664e+00 1.0368e-02 9.0769e-01 2.5875e+00 7.2736e-03 7.1678e-01 2.2770e+00 5.3492e-03 5.8116e-01 2.0192e+00 4.0891e-03 4.8185e-01 1.8022e+00 3.2271e-03 4.0724e-01 1.6170e+00 2.6153e-03 3.4994e-01 1.4568e+00 2.1675e-03 3.0511e-01 1.3166e+00 1.8310e-03 2.6946e-01 1.1925e+00 1.5727e-03 2.4073e-01 1.0814e+00 1.3705e-03 2.1731e-01 9.8112e-01 1.2097e-03 1.9802e-01 8.8971e-01 1.0800e-03 1.8202e-01 8.0572e-01 9.7432e-04 1.6865e-01 7.2796e-01 8.8726e-04 1.5743e-01 6.5545e-01 8.1497e-04 1.4798e-01 5.8737e-01 7.5457e-04 1.4002e-01 5.2304e-01 7.0384e-04 1.3332e-01 4.6188e-01 6.6110e-04 1.2769e-01 4.0340e-01 6.2504e-04 1.2300e-01 3.4716e-01 5.9462e-04 1.1914e-01 2.9278e-01 5.6905e-04 1.1602e-01 2.3993e-01 5.4769e-04 1.1357e-01 1.8830e-01 5.3002e-04 1.1174e-01 1.3761e-01 5.1565e-04 1.1049e-01 8.7597e-02 5.0427e-04 1.0980e-01 3.8005e-02 4.9565e-04 1.0965e-01 -1.1403e-02 4.8960e-04 1.1005e-01 -6.0866e-02 4.8602e-04 1.1099e-01 -1.1062e-01 4.8482e-04 1.1251e-01 -1.6092e-01 4.8598e-04 1.1462e-01 -2.1201e-01 4.8953e-04 1.1737e-01 -2.6417e-01 4.9553e-04 1.2083e-01 -3.1768e-01 5.0410e-04 1.2506e-01 -3.7288e-01 5.1541e-04 1.3017e-01 -4.3010e-01 5.2968e-04 1.3628e-01 -4.8977e-01 5.4722e-04 1.4354e-01 -5.5233e-01 5.6842e-04 1.5216e-01 -6.1832e-01 5.9377e-04 1.6240e-01 -6.8836e-01 6.2387e-04 1.7457e-01 -7.6320e-01 6.5951e-04 1.8910e-01 -8.4372e-01 7.0165e-04 2.0656e-01 -9.3099e-01 7.5154e-04 2.2767e-01 -1.0263e+00 8.1076e-04 2.5343e-01 -1.1314e+00 8.8134e-04 2.8521e-01 -1.2482e+00 9.6589e-04 3.2491e-01 -1.3795e+00 1.0679e-03 octave:20> octave:20> [tout,yout]=rk23(f,tspan,y0); octave:21> E=(yout(:,1).^2+yout(:,2).^2+yout(:,3).^2+1)./(2*yout(:,1)); octave:22> plot(tout,E,'*') octave:23> options.AbsTol=1e-2; octave:24> options.RelTol=1e-2; octave:25> [tout,yout]=rk23(f,tspan,y0,options); warning: time step rejected warning: time step rejected warning: time step rejected warning: time step rejected warning: time step rejected warning: time step rejected warning: time step rejected warning: time step rejected warning: time step rejected octave:26> plot(tout,E,'*') error: __plt2vv__: vector lengths must match error: called from: error: /usr/share/octave/3.8.1/m/plot/draw/private/__plt__.m at line 484, column 5 error: /usr/share/octave/3.8.1/m/plot/draw/private/__plt__.m at line 243, column 14 error: /usr/share/octave/3.8.1/m/plot/draw/private/__plt__.m at line 113, column 17 error: /usr/share/octave/3.8.1/m/plot/draw/plot.m at line 220, column 10 octave:26> E=(yout(:,1).^2+yout(:,2).^2+yout(:,3).^2+1)./(2*yout(:,1)); octave:27> plot(tout,E,'*') octave:28> help lsode 'lsode' is a built-in function from the file libinterp/corefcn/lsode.cc -- Built-in Function: [X, ISTATE, MSG] = lsode (FCN, X_0, T) -- Built-in Function: [X, ISTATE, MSG] = lsode (FCN, X_0, T, T_CRIT) Solve the set of differential equations dx -- = f (x, t) dt with x(t_0) = x_0 The solution is returned in the matrix X, with each row corresponding to an element of the vector T. The first element of T should be t_0 and should correspond to the initial state of the system X_0, so that the first row of the output is X_0. The first argument, FCN, is a string, inline, or function handle that names the function f to call to compute the vector of right hand sides for the set of equations. The function must have the form XDOT = f (X, T) in which XDOT and X are vectors and T is a scalar. If FCN is a two-element string array or a two-element cell array of strings, inline functions, or function handles, the first element names the function f described above, and the second element names a function to compute the Jacobian of f. The Jacobian function must have the form JAC = j (X, T) in which JAC is the matrix of partial derivatives | df_1 df_1 df_1 | | ---- ---- ... ---- | | dx_1 dx_2 dx_N | | | | df_2 df_2 df_2 | | ---- ---- ... ---- | df_i | dx_1 dx_2 dx_N | jac = ---- = | | dx_j | . . . . | | . . . . | | . . . . | | | | df_N df_N df_N | | ---- ---- ... ---- | | dx_1 dx_2 dx_N | The second and third arguments specify the initial state of the system, x_0, and the initial value of the independent variable t_0. The fourth argument is optional, and may be used to specify a set of times that the ODE solver should not integrate past. It is useful for avoiding difficulties with singularities and points where there is a discontinuity in the derivative. After a successful computation, the value of ISTATE will be 2 (consistent with the Fortran version of LSODE). If the computation is not successful, ISTATE will be something other than 2 and MSG will contain additional information. You can use the function 'lsode_options' to set optional parameters for 'lsode'. See also: daspk, dassl, dasrt. 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:29> octave:29> edit normest octave:30> octave:30> octave:30> quit