{ "format_version": 1, "description": "Clamp-at-commit Euler/AB and clamp-every-stage RK4, including both relaxation references.", "initial": [ 0.02, 0.37, 0.81, 0.98 ], "time": 0.25, "dt": 0.4, "synthetic_derivative": "k_i(A,t)=0.34-0.45*A_i+(i+1)*0.08*t", "euler": { "k1": [ 0.35100000000000003, 0.21350000000000002, 0.035499999999999976, -0.020999999999999977 ], "next": [ 0.16040000000000001, 0.4554, 0.8242, 0.9716 ] }, "ab3_startup": { "methods": [ "Euler", "AB2", "AB3" ], "states": [ [ 0.02, 0.37, 0.81, 0.98 ], [ 0.16040000000000001, 0.4554, 0.8242, 0.9716 ], [ 0.282092, 0.556142, 0.892166, 1.0 ], [ 0.39776626000000004, 0.6618190100000001, 0.97742673, 1.0 ] ], "derivatives": [ [ 0.35100000000000003, 0.21350000000000002, 0.035499999999999976, -0.020999999999999977 ], [ 0.31982, 0.23907, 0.12510999999999997, 0.11078000000000005 ], [ 0.2970586, 0.2577361, 0.1905253, 0.22600000000000003 ] ], "ab2_combination": [ 0.30423, 0.251855, 0.16991499999999998, 0.17667000000000005 ], "ab3_combination": [ 0.28918565, 0.26419252500000007, 0.21315182500000004, 0.27670999999999996 ] }, "rk4": { "stage_states": [ [ 0.02, 0.37, 0.81, 0.98 ], [ 0.09020000000000002, 0.4127, 0.8171, 0.9758 ], [ 0.087082, 0.415257, 0.826061, 0.988978 ], [ 0.15472523999999999, 0.46005374, 0.84050902, 0.99558396 ] ], "derivatives": [ [ 0.35100000000000003, 0.21350000000000002, 0.035499999999999976, -0.020999999999999977 ], [ 0.33541, 0.22628500000000001, 0.08030499999999997, 0.04489000000000004 ], [ 0.3368131, 0.22513435000000004, 0.07627255000000001, 0.03895990000000005 ], [ 0.322373642, 0.23697581700000003, 0.11777094099999999, 0.09998721799999999 ] ], "combined": [ 0.33630330699999994, 0.22555241950000002, 0.07773767349999999, 0.04111450300000003 ], "next": [ 0.15452132279999997, 0.4602209678, 0.8410950694, 0.9964458012 ] }, "relaxation_target": "S_i(A)=0.1+0.65*A_(i-1)+0.2*A_(i+1), periodic", "rk4_relaxation_stage_state": { "reference": "stage_state", "stage_states": [ [ 0.02, 0.37, 0.81, 0.98 ], [ 0.1782, 0.351, 0.7553000000000001, 0.9101 ], [ 0.136713, 0.373178, 0.760974, 0.923297 ], [ 0.27522626000000006, 0.3571521, 0.7165004400000001, 0.85947148 ] ], "targets": [ [ 0.8109999999999999, 0.275, 0.5365, 0.6305000000000001 ], [ 0.761765, 0.36689000000000005, 0.51017, 0.6265850000000001 ], [ 0.77477865, 0.34105825, 0.5272251000000001, 0.6219757 ], [ 0.7300868819999999, 0.42219715700000005, 0.504043161, 0.620770538 ] ], "derivatives": [ [ 0.7909999999999999, -0.09499999999999997, -0.2735000000000001, -0.3494999999999999 ], [ 0.583565, 0.01589000000000007, -0.24513000000000007, -0.28351499999999996 ], [ 0.63806565, -0.03211975, -0.23374889999999993, -0.3013213 ], [ 0.4548606219999999, 0.06504505700000007, -0.2124572790000001, -0.23870094199999992 ] ], "combined": [ 0.6148536536666667, -0.010402407166666627, -0.24061917983333336, -0.2929789236666666 ], "next": [ 0.2659414614666667, 0.3658390371333333, 0.7137523280666667, 0.8628084305333333 ] }, "rk4_relaxation_step_origin": { "reference": "step_origin", "stage_states": [ [ 0.02, 0.37, 0.81, 0.98 ], [ 0.1782, 0.351, 0.7553000000000001, 0.9101 ], [ 0.168353, 0.369378, 0.7500340000000001, 0.909317 ], [ 0.3179726600000001, 0.3657745, 0.69478364, 0.83647708 ] ], "targets": [ [ 0.8109999999999999, 0.275, 0.5365, 0.6305000000000001 ], [ 0.761765, 0.36689000000000005, 0.51017, 0.6265850000000001 ], [ 0.7649316500000001, 0.35943625, 0.5219591, 0.6211927 ], [ 0.716865002, 0.4456389570000001, 0.505048841, 0.615203898 ] ], "derivatives": [ [ 0.7909999999999999, -0.09499999999999997, -0.2735000000000001, -0.3494999999999999 ], [ 0.741765, -0.003109999999999946, -0.29983000000000004, -0.3534149999999999 ], [ 0.7449316500000001, -0.010563749999999983, -0.28804090000000004, -0.35880729999999994 ], [ 0.696865002, 0.07563895700000012, -0.304951159, -0.364796102 ] ], "combined": [ 0.7435430503333333, -0.007784757166666619, -0.2923654931666667, -0.3564567836666666 ], "next": [ 0.31741722013333334, 0.36688609713333337, 0.6930538027333334, 0.8374172865333334 ] } }