Numerical Investigation on Convergence Rate of Singular Boundary Method

<div>Relative errors of Example <a href="https://static.hindawi.com/articles/mpe/volume-2016/3564632/figures/#ex5">5</a> by using the SBM and the BEM. <svg height="11.9316pt" id="M164" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 57.6959 11.9316" width="57.6959pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M416 501L399 642C356 655 314 665 271 665C140 665 63 582 63 486C63 372 163 325 229 290C304 250 359 217 359 142C359 70 316 25 240 25C138 25 94 125 78 186L44 178C52 123 64 45 72 21C81 16 96 8 121 0S179 -15 220 -15C353 -15 445 68 445 176C445 289 350 335 270 375C191 414 143 449 143 520C143 572 177 627 253 627C340 627 366 556 382 495L416 501Z" id="g58-81"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="484" vert-adv-y="484"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.923,3.132)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z" id="g58-64"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="598" vert-adv-y="598"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,18.365,3.132)"><path d="M871 0V33C783 41 780 45 777 152L768 506C765 610 771 609 860 617V650H683L453 157L228 650H59V617C150 609 154 606 146 481L132 275C124 170 117 125 112 93C105 50 84 39 27 34V0H267V34C200 39 176 48 173 93C170 130 171 172 176 256L190 540H192L414 8H438L682 554H685L689 152C689 45 686 41 604 33V0H871Z" id="g58-75"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="902" vert-adv-y="902"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.77,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,42.033,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,48.274,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,51.238,0)"><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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>; 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Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Numerical Investigation on Convergence Rate of Singular Boundary Method 