A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/stni/volume-2018/7105245/figures/7105245.fig.002a.svgz" name="7105245.fig.002a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>The time to the neutron peak and the neutron density at that peak for sinusoidal reactivity for fast reactor I with <svg height="11.7978pt" id="M253" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 47.0285 11.7978" width="47.0285pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M671 0V28C608 36 593 47 562 130C495 309 432 486 368 665L336 656C270 481 202 311 134 139C98 47 84 39 20 28V0H241V28C167 38 156 47 178 115C217 236 276 383 327 530H329C375 398 437 223 484 92C499 47 489 37 424 28V0H671Z" id="g113-140"></path></g><g transform="matrix(.013,0,0,-0.013,12.543,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,23.806,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,30.046,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.0091,0,0,-0.0091,36.332,-5.741)"><path d="M556 236V289H56V236H556Z" id="g54-33"></path></g><g transform="matrix(.0091,0,0,-0.0091,41.892,-5.741)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z" id="g50-55"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/stni/volume-2018/7105245/figures/7105245.fig.002b.svgz" name="7105245.fig.002b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>The time to the neutron peak and the neutron density at that peak for sinusoidal reactivity for fast reactor II with <svg height="11.7978pt" id="M254" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 47.0285 11.7978" width="47.0285pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M671 0V28C608 36 593 47 562 130C495 309 432 486 368 665L336 656C270 481 202 311 134 139C98 47 84 39 20 28V0H241V28C167 38 156 47 178 115C217 236 276 383 327 530H329C375 398 437 223 484 92C499 47 489 37 424 28V0H671Z" id="g113-140"></path></g><g transform="matrix(.013,0,0,-0.013,12.543,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,23.806,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,30.046,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.0091,0,0,-0.0091,36.332,-5.741)"><path d="M556 236V289H56V236H556Z" id="g54-33"></path></g><g transform="matrix(.0091,0,0,-0.0091,41.892,-5.741)"><path d="M253 635C142 635 71 555 71 471C71 401 113 353 178 316C144 294 106 267 91 252C70 231 46 202 46 157C46 51 132 -12 241 -12C328 -12 442 52 442 168C442 257 379 305 311 343C354 373 380 398 388 407C406 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 563 340 481C340 423 313 387 279 360C207 394 148 427 148 499C148 549 182 600 240 600ZM252 23C188 23 129 73 129 163C129 217 162 266 211 298C289 260 360 217 360 144C360 69 312 23 252 23Z" id="g50-57"></path></g></svg></td></tr></table>

Science and Technology of Nuclear Installations

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Figure 2

Figure 2: A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems 