Local RBF-FD-Based Mesh-free Scheme for Singularly Perturbed Convection-Diffusion-Reaction Models with Variable Coefficients

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center" colspan="6">Corresponding CPU time</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">Time</td><td class="align_center"><span style="width: 41.612ptpx;"><svg height="11.7978pt" id="M173" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 41.612 11.7978" width="41.612pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.963,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.226,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,26.466,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.026,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,36.458,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 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275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z"></path></g></svg></span></td></tr><tr><td class="align_left">0.1</td><td class="align_center">0.456</td><td class="align_center">0.440</td><td class="align_center">0.448</td><td class="align_center">0.408</td><td class="align_center">0.367</td><td class="align_center">0.418</td></tr><tr><td class="align_left">0.5</td><td class="align_center">1.32</td><td class="align_center">1.32</td><td class="align_center">1.34</td><td class="align_center">1.28</td><td class="align_center">1.29</td><td class="align_center">1.52</td></tr><tr><td class="align_left">1.0</td><td class="align_center">2.56</td><td class="align_center">2.67</td><td class="align_center">2.65</td><td class="align_center">2.67</td><td class="align_center">2.47</td><td class="align_center">2.88</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>CPU time at different time and <span class="nowrap"><svg height="6.1673pt" id="M172" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.44961 6.1673" width="5.44961pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g></svg>.</span></div>

Journal of Mathematics

tab4

Table 4

Table 4: Local RBF-FD-Based Mesh-free Scheme for Singularly Perturbed Convection-Diffusion-Reaction Models with Variable Coefficients 