A New Precursor Integral Method for Solving Space-Dependent Kinetic Equations in Neutronic and Thermal-Hydraulic Coupling System

Table 3

Comparison of relative power (percentage error) between independent precursor methods and precursor elimination methods for ramp reactivity insertion.

		Reference	Independent variables	Zero-order Taylor expansion	First-order Taylor expansion	Exponential expansion
0.0	—	1.00000	1.00000	1.00000	1.00000	1.00000
0.1	10.0	1.30832	1.30935 (−7.9e − 2)	1.30906 (−5.6e − 2)	1.30921 (−6.7e − 2)	1.30922 (−6.8e − 2)
	20.0	—	1.31036 (−1.5e − 1)	1.30977 (−1.1e − 1)	1.31007 (−1.3e − 1)	1.31009 (−1.3e − 1)
0.2	10.0	1.95908	1.96410 (+2.6e − 1)	1.96273 (+1.8e − 1)	1.96342 (+2.3e − 1)	1.96346 (+2.2e − 1)
	20.0	—	1.96842 (+4.7e − 1)	1.96564 (+3.3e − 1)	1.96704 (+4.1e − 1)	1.96712 (+4.1e − 1)
0.3	10.0	2.07503	2.07578 (+3.6e − 2)	2.07403 (−4.8e − 2)	2.07491 (−5.6e − 3)	2.07496 (−3.1e − 3)
	20.0	—	2.07636 (−6.4e − 1)	2.07286 (−1.0e − 1)	2.07462 (−1.9e − 2)	2.07472 (−1.5e − 2)
0.4	10.0	2.09239	2.09326 (+4.1e − 2)	2.09147 (−4.4e − 2)	2.09237 (−8.1e − 4)	2.09242 (+1.6e − 3)
	20.0	—	2.09416 (+8.4e − 2)	2.09058 (−8.6e − 2)	2.09238 (−1.9e − 4)	2.09248 (+4.3e − 3)
0.5	10.0	2.10988	2.11077 (+4.1e − 2)	2.10894 (−4.4e − 2)	2.10987 (−8.0e − 4)	2.10992 (+1.7e − 3)
	20.0	—	2.11169 (+8.5e − 2)	2.10803 (−8.7e − 2)	2.10988 (−9.7e − 5)	2.10998 (+4.4e − 3)