time exact result rk4-fehlberg difference trunc err tau sum of h*tau h=0.2 ----- 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 2.0000000e-01 2.6812802e-02 2.6801052e-02 1.1749792e-05 3.7049666e-05 7.4099333e-06 4.0000000e-01 1.5077784e-01 1.5074452e-01 3.3318050e-05 8.1378629e-05 2.3685659e-05 6.0000000e-01 4.9601957e-01 4.9594254e-01 7.7021798e-05 1.7756032e-04 5.9197724e-05 8.0000000e-01 1.3308570e+00 1.3306899e+00 1.6711372e-04 3.7957101e-04 1.3511193e-04 1.0000000e+00 3.2190993e+00 3.2187476e+00 3.5174318e-04 7.9552603e-04 2.9421713e-04 1.2000000e+00 7.3232756e+00 7.3225493e+00 7.2626381e-04 1.6400724e-03 6.2223161e-04 1.4000000e+00 1.6007152e+01 1.6005673e+01 1.4785551e-03 3.3363828e-03 1.2895082e-03 1.6000000e+00 3.4024547e+01 3.4021571e+01 2.9768610e-03 6.7138818e-03 2.6322845e-03 1.8000000e+00 7.0851146e+01 7.0845207e+01 5.9394591e-03 1.3390163e-02 5.3103171e-03 2.0000000e+00 1.4523510e+02 1.4522334e+02 1.1761364e-02 2.6506306e-02 1.0611578e-02 h=0.1 ----- 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 1.0000000e-01 5.7520540e-03 5.7518082e-03 2.4577249e-07 1.8521891e-06 1.8521891e-07 2.0000000e-01 2.6812802e-02 2.6812238e-02 5.6423470e-07 2.7480999e-06 4.6002890e-07 3.0000000e-01 7.1144528e-02 7.1143528e-02 9.9976718e-07 4.0939505e-06 8.6942395e-07 4.0000000e-01 1.5077784e-01 1.5077622e-01 1.6136129e-06 6.0858901e-06 1.4780130e-06 5.0000000e-01 2.8361652e-01 2.8361403e-01 2.4913879e-06 9.0038791e-06 2.3784009e-06 6.0000000e-01 4.9601957e-01 4.9601581e-01 3.7535424e-06 1.3246028e-05 3.7030037e-06 7.0000000e-01 8.2648087e-01 8.2647530e-01 5.5699671e-06 1.9376758e-05 5.6406795e-06 8.0000000e-01 1.3308570e+00 1.3308488e+00 8.1804054e-06 2.8194247e-05 8.4601042e-06 9.0000000e-01 2.0897744e+00 2.0897625e+00 1.1922976e-05 4.0824739e-05 1.2542578e-05 1.0000000e+00 3.2190993e+00 3.2190820e+00 1.7274011e-05 5.8854271e-05 1.8428005e-05 1.1000000e+00 4.8847071e+00 4.8846822e+00 2.4903643e-05 8.4512434e-05 2.6879249e-05 1.2000000e+00 7.3232756e+00 7.3232399e+00 3.5753333e-05 1.2092846e-04 3.8972095e-05 1.3000000e+00 1.0871510e+01 1.0871459e+01 5.1143849e-05 1.7248774e-04 5.6220868e-05 1.4000000e+00 1.6007152e+01 1.6007079e+01 7.2925574e-05 2.4532767e-04 8.0753635e-05 1.5000000e+00 2.3406446e+01 2.3406342e+01 1.0368752e-04 3.4802680e-04 1.1555632e-04 1.6000000e+00 3.4024547e+01 3.4024400e+01 1.4704777e-04 4.9256162e-04 1.6481248e-04 1.7000000e+00 4.9207907e+01 4.9207699e+01 2.0805663e-04 6.9563413e-04 2.3437589e-04 1.8000000e+00 7.0851146e+01 7.0850852e+01 2.9375606e-04 9.8051241e-04 3.3242713e-04 1.9000000e+00 1.0161581e+02 1.0161540e+02 4.1395508e-04 1.3795806e-03 4.7038519e-04 2.0000000e+00 1.4523510e+02 1.4523452e+02 5.8230405e-04 1.9378697e-03 6.6417216e-04