Highly Efficacious Sixth-Order Compact Approach with Nonclassical Boundary Specifications for the Heat Equation

<div>Exact solution in the (a) and its approximation in the (b) and absolute error curve in the (c) for <svg height="11.5825pt" id="M427" style="vertical-align:-2.51599pt" version="1.1" viewbox="-0.0498162 -9.06651 43.5867 11.5825" width="43.5867pt" 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="M226 -184L251 -206C307 -150 362 -94 408 -31C419 6 424 45 428 84C433 137 435 192 435 246C435 303 432 360 428 417C386 430 345 448 312 478C262 443 197 397 164 371V503C164 572 204 633 255 678L238 689C237 689 157 630 117 601C109 627 93 676 93 677C92 677 85 675 81 675C93 472 88 268 76 65C87 50 113 5 131 -26L213 49C196 73 173 105 164 121C164 194 164 267 164 341C195 360 241 390 258 390C291 390 320 373 346 354C350 300 356 221 356 193C356 132 354 71 346 11C341 -26 335 -64 318 -98C311 -110 303 -121 292 -129L226 -184Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.405,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.668,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.908,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.872,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,37.112,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g></svg> for Example <a href="https://static.hindawi.com/articles/mpe/volume-2022/8224959/figures/#ex4">4</a>.</div>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Highly Efficacious Sixth-Order Compact Approach with Nonclassical Boundary Specifications for the Heat Equation 