Research Article
A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems
(a) Reactor power (watts): comparison between the SCS, BEFD, and SKINATH results |
| | Methods | | SKINATH | BEFD | SCS |
| | 0.000 | 1.000E-02 | 1.000000000E-02 | 1.00000000000E-02 | | 1.000 | 1.391E-02 | 1.390664400E-02 | 1.39066439992E-02 | | 10.00 | 1.033E-01 | 1.033074569E-01 | 1.03307456949E-01 | | 100.0 | 7.946E-01 | 7.946137382E-01 | 7.94613738201E-01 | | 250.0 | 2.118E-03 | 2.118680532E-03 | 2.11868053231E-03 | | 500.0 | 9.819E-01 | 9.818854372E-01 | 9.81885437265E-01 | | 750.0 | 4.033E+00 | 4.033472004E+00 | 4.03347200416E+00 | | 1000 | 7.680E+00 | 7.680950791E+00 | 7.68095079127E+00 | | 1500 | — | 1.502421669E+01 | 1.50242166936E+01 | | 2000 | — | 1.358851928E+01 | 1.35885192813E+01 | | 2500 | — | 1.348250322E+01 | 1.34825032231E+01 | | 3000 | — | 1.359755709E+01 | 1.35975570943E+01 | | 4000 | — | 1.357214030E+01 | 1.35721402958E+01 | | 5000 | — | — | 1.35731363004E+01 |
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(b) Reactivity ($): comparison between the SCS, BEFD, and SKINATH results |
| | Methods | | SKINATH | BEFD | SCS |
| | 0.000 | 4.300E-02 | 4.300000000E-02 | 4.30000000000E-02 | | 1.000 | 4.230E-02 | 4.299982607E-02 | 4.29998260709E-02 | | 10.00 | 4.299E-02 | 4.299416065E-02 | 4.29941606543E-02 | | 100.0 | -2.950E-02 | -2.949530409E-02 | -2.94953040871E-02 | | 250.0 | 6.388E-03 | 6.388467468E-03 | 6.38846746738E-03 | | 500.0 | -4.826E-03 | -4.825173107E-03 | -4.82517310699E-03 | | 750.0 | -1.858E-03 | -1.857286712E-03 | -1.85728671222E-03 | | 1000 | 1.379E-03 | 1.379148486E-03 | 1.37914848596E-03 | | 1500 | — | 4.962590743E-04 | 4.96259074364E-04 | | 2000 | — | -2.104995975E-04 | -2.10499597521E-04 | | 2500 | — | 3.094249800E-05 | 3.09424979793E-05 | | 3000 | — | 3.819718029E-06 | 3.81971800210E-06 | | 4000 | — | 5.947391521E-07 | 5.94739152658E-07 | | 5000 | — | — | -3.71867594560E-08 |
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(c) Temperature (°C): comparison between the SCS, BEFD, and SKINATH results |
| | Methods | | SKINATH | BEFD | SCS |
| | 0.000 | 2.000E+01 | 2.000000000E+01 | 2.00000000000E+01 | | 1.000 | 2.000E+01 | 2.000005684E+01 | 2.00000568396E+01 | | 10.00 | 2.000E+01 | 2.000190828E+01 | 2.00019082829E+01 | | 100.0 | 4.369E+01 | 4.369127585E+01 | 4.36912758455E+01 | | 250.0 | 3.196E+01 | 3.196455312E+01 | 3.19645531152E+01 | | 500.0 | 3.563E+01 | 3.562914154E+01 | 3.56291415382E+01 | | 750.0 | 3.466E+01 | 3.465924402E+01 | 3.46592440236E+01 | | 1000 | 3.360E+01 | 3.360158546E+01 | 3.36015854621E+01 | | 1500 | — | 3.389011141E+01 | 3.38901114136E+01 | | 2000 | — | 3.412107830E+01 | 3.41210782998E+01 | | 2500 | — | 3.404217565E+01 | 3.40421756543E+01 | | 3000 | — | 3.405103931E+01 | 3.40510393078E+01 | | 4000 | — | 3.405209322E+01 | 3.40520932225E+01 | | 5000 | — | — | 3.40522997342E+01 |
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