Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left">Method</td><td class="align_center">C-Time</td><td class="align_center"><span style="width: 16.9882ptpx;"><svg height="16.4744pt" id="M61" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 16.9882 16.4744" width="16.9882pt" 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="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.382,-6.049)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 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244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.605,-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"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.037,-5.741)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">MWM1</td><td class="align_center">2.119</td><td class="align_center">0.07</td><td class="align_center">0.02</td><td class="align_center">0.1</td><td class="align_center">0.1</td><td class="align_center">2.125</td></tr><tr><td class="align_left">MWM2</td><td class="align_center">0.115</td><td class="align_center">3.5<i>e</i> − 324</td><td class="align_center">2.0<i>e</i> − 319</td><td class="align_center">0.005</td><td class="align_center">0.005</td><td class="align_center">2.968</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Residual error for finding all distinct roots.</div>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications 

Table 2 | Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications 