Reproducing Kernel Method with Global Derivative

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left"><span style="width: 6.6501ptpx;"><svg height="6.1673pt" id="M200" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.6501 6.1673" width="6.6501pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g></svg></span></td><td class="align_center">Maximum absolute error</td><td class="align_center"><span style="width: 27.6514ptpx;"><svg height="12.5794pt" id="M201" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 27.6514 12.5794" width="27.6514pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M699 369C699 549 575 666 407 666C186 666 23 488 23 278C23 101 145 -16 312 -16C535 -16 699 153 699 369ZM600 373C600 210 500 19 321 19C186 19 120 129 120 272C120 450 232 631 399 631C541 631 600 522 600 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.559,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.811,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.309,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">2</td><td class="align_center">0.0833</td><td class="align_center"><span style="width: 24.1616ptpx;"><svg height="3.39444pt" id="M202" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -3.34462 24.1616 3.39444" width="24.1616pt" 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="M872 201V252H50V201H872Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.031,0)"><path d="M872 201V252H50V201H872Z"></path></g></svg></span></td></tr><tr><td class="align_left">4</td><td class="align_center">0.0167</td><td class="align_center">2.32</td></tr><tr><td class="align_left">8</td><td class="align_center">0.0035</td><td class="align_center">2.26</td></tr><tr><td class="align_left">16</td><td class="align_center">0.0008</td><td class="align_center">2.18</td></tr><tr><td class="align_left">32</td><td class="align_center">0.0002</td><td class="align_center">2.11</td></tr><tr><td class="align_left">64</td><td class="align_center">0.0000</td><td class="align_center">2.06</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Rate of convergence for Example <a href="https://static-preview.hindawi.com/articles/jfs/volume-2023/2726735/figures/#ex2" target="_blank">2</a> with <svg height="12.7178pt" id="M199" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 49.041 12.7178" width="49.041pt" 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="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.398,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.896,0)"><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(.013,0,0,-0.013,19.163,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.293,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.556,0)"><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(.013,0,0,-0.013,45.823,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></div>

Journal of Function Spaces

Reproducing Kernel Method with Global Derivative

Table 2