Research Article
A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems
Table 3
Comparison between the SCS method of order ten and various numerical methods for
ramp reactivity (moderately fast reactor).
| | Methods | | Time (s) | | 0.00 | 2.00 | 4.00 | 6.00 | 8.00 | 10.0 | 11.0 |
| | - weighting | 1.0E-4 | 1.0000E+00 | 1.3382E+00 | 2.2283E+00 | 5.5815E+00 | 4.2781E+01 | 4.5109E+05 | 1.7919E+16 | | GRK | 5.6E-2 | 1.0000E+00 | 1.3382E+00 | 2.2284E+00 | 5.5820E+00 | 4.2786E+01 | 4.5115E+05 | 1.7904E+16 | | AIM | 1.0E-3 | 1.0000E+00 | 1.3382E+00 | 2.2284E+00 | 5.5820E+00 | 4.2786E+01 | 4.5116E+05 | 1.7916E+16 | | PCA | 1.0E-2 | 1.0000E+00 | 1.3382E+00 | 2.2278E+00 | 5.5802E+00 | 4.2772E+01 | — | — | | CORE | 1.0E-4 | 1.0000E+00 | 1.3382E+00 | 2.2285E+00 | 5.5822E+00 | 4.2790E+01 | 4.5144E+05 | 1.7957E+16 | | BBF | 1.0E-1 | 1.0000E+00 | 1.338200E+00 | 2.228442E+00 | 5.582052E+00 | 4.278629E+01 | 4.504121E+05 | — | | Hermite Polynomial | 1.0E-4 | 1.0000E+00 | 1.338200E+00 | 2.228440E+00 | 5.582052E+00 | 4.278630E+01 | 4.511630E+05 | — | | GAEM | 1.0E-1 | 1.0000E+00 | 1.338196E+00 | 2.228435E+00 | 5.582036E+00 | 4.278619E+01 | 4.511648E+05 | — | | Pade’ | 1.0E-3 | 1.0000E+00 | 1.338198E+00 | 2.228436E+00 | 5.582037E+00 | 4.278634E+01 | 4.511685E+05 | — | | ET | 1.0E-3 | 1.0000E+00 | 1.3382E+00 | 2.2284E+00 | 5.5820E+00 | 4.2786E+01 | 4.5116E+05 | — | | PWS | 0.01 | 1.0000E+00 | 1.338200050E+00 | 2.228441896E+00 | 5.582052448E+00 | 4.278629573E+01 | 4.511636239E+05 | 1.792213607E+16 | | CATS | | 1.0000E+00 | 1.338200050E+00 | 2.228441897E+00 | 5.582052449E+00 | 4.278629573E+01 | 4.511636239E+05 | 1.792213607E+16 | | Accurate Solution | 0.001 | 1.0000E+00 | 1.3382E+00 | 2.2284E+00 | 5.582E+00 | 4.2786E+01 | 4.5117E+05 | — | | EPCA | 2.0E-3 | 1.0000E+00 | 1.338200050E+00 | 2.228441897E+00 | 5.582052450E+00 | 4.278629574E+01 | 4.511636240E+05 | 1.792213608E+16 | | BEFD | Variable | 1.0000E+00 | 1.338200050E+00 | 2.228441897E+00 | 5.582052449E+00 | 4.278629573E+01 | 4.511636239E+05 | 1.792213607E+16 | | ITS2 | Variable | 1.0000E+00 | 1.338200050E+00 | 2.228441897E+00 | 5.582052449E+00 | 4.278629573E+01 | 4.511636239E+05 | 1.792213608E+16 | | HWOM | — | 1.0000E+00 | 1.338200011E+00 | 2.228441300E+00 | 5.582043255E+00 | 4.278584501E+01 | 4.522953180E+05 | 1.828233653E+16 | | TTM | 1.0E-5 | 1.0000E+00 | 1.338200050E+00 | 2.228441896E+00 | 5.582052447E+00 | 4.278629572E+01 | 4.511636238E+05 | 1.792213607E+16 | | TFS | 1.0E-2 | 1.0000E+00 | 1.338200050E+00 | 2.228441897E+00 | 5.582052449E+00 | 4.278629573E+01 | 4.511636239E+05 | 1.792213607E+16 | | Modified ETD | 1.0E-2 | 1.0000E+00 | 1.338200E+00 | 2.228442E+00 | 5.582052E+00 | 4.278630E+01 | 4.511636E+05 | — |
| | SCS | 1.0E-2 | 1.0000E+00 | 1.338200050E+00 | 2.228441897E+00 | 5.582052449E+00 | 4.278629573E+01 | 4.511636239E+05 | 1.792213607E+16 |
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is variable, the total number of iteration was 372, and the smallest time calculation per step was 0.0156 s. |
