A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Method</td><td class="align_center"><span style="width: 67.9809ptpx;"><svg height="12.5794pt" id="M150" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 67.9809 12.5794" width="67.9809pt" 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="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.145,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.408,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.827,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.029,3.132)"><path d="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 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version="1.1" viewbox="-0.0498162 -9.28833 67.9809 12.5794" width="67.9809pt" 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="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.145,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.408,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.827,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 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402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,59.953,3.132)"><path d="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z"></path></g><g transform="matrix(.013,0,0,-0.013,64.306,0)"><path d="M162 -163V703H101V-163H162Z"></path></g></svg></span></td><td class="align_center" rowspan="2"><span style="width: 41.7727ptpx;"><svg height="12.997pt" id="M153" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -9.7059 41.7727 12.997" width="41.7727pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.723,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 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class="align_left">(1)</td><td class="align_center">8.07e-07</td><td class="align_center">1.15e-12</td><td class="align_center">2.03e-01</td><td class="align_center">1.04e-06</td><td class="align_center">1.34e-10</td><td class="align_center">1.71e-01</td></tr><tr><td class="align_left">(2)</td><td class="align_center">1.77e-77</td><td class="align_center">6.63e-307</td><td class="align_center">4.84e-01</td><td class="align_center">Other sol.</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">(4)</td><td class="align_center">4.02e-334</td><td class="align_center">1.32e-2001</td><td class="align_center">2.03e-01</td><td class="align_center">1.16e-410</td><td class="align_center">3.76e-2457</td><td class="align_center">1.10e-01</td></tr><tr><td class="align_left">(5)</td><td class="align_center">Diverge</td><td class="align_center">—</td><td class="align_center">—</td><td class="align_center">1.94e-411</td><td class="align_center">8.30e-2462</td><td class="align_center">3.91e-01</td></tr><tr><td class="align_left">(6)</td><td class="align_center">4.56e-138</td><td class="align_center">5.43e-825</td><td class="align_center">2.81e-01</td><td class="align_center">2.72e-449</td><td class="align_center">4.40e-2689</td><td class="align_center">2.03e-01</td></tr><tr><td class="align_left">(7)</td><td class="align_center">1.08e-1166</td><td class="align_center">4.93e-6997</td><td class="align_center">2.34e-01</td><td class="align_center">2.77e-675</td><td class="align_center">7.15e-4045</td><td class="align_center">1.40e-01</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison of several methods with the proposed method under different initial guesses and different numbers of iterations for the blood rheology model given in (<a href="https://static-preview.hindawi.com/articles/cmmm/volume-2022/7656451/figures/#EEq30" target="_blank">38</a>).</div>

Computational and Mathematical Methods in Medicine

tab1

Table 1

Table 1: A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics 