A New Numerical Method to Solve Some <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3442pt" id="M1" height="15.5972pt" version="1.1" viewBox="-0.0657574 -11.253 37.2822 15.5972" width="37.2822pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g190-81" d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"/></g><g transform="matrix(.017,0,0,-0.017,9.575,0)"><path id="g190-69" d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"/></g><g transform="matrix(.017,0,0,-0.017,22.032,0)"><path id="g190-70" d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z"/></g><g transform="matrix(.012,0,0,-0.012,31.899,4.134)"><path id="g50-116" d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"/></g></svg> in the Unit Ball and Comparison with the Finite Element and the Exact Solution

<div>The <svg height="12.689pt" id="M354" style="vertical-align:-3.40067pt" version="1.1" viewbox="-0.0498162 -9.28833 28.9618 12.689" width="28.9618pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.396,3.132)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.475,0)"><path d="M387 138L374 114C336 54 316 33 240 33H141C223 167 303 295 385 423L379 437H149C112 437 100 443 94 458H73C65 415 50 352 39 314L64 305L78 332C106 388 119 403 191 403C214 403 246 403 280 403C198 270 117 142 31 15L38 0H367C382 40 399 86 413 125L387 138Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.935,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.262,0)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.293,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g></svg> solution at <span class="nowrap"><svg height="8.55521pt" id="M355" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 41.2379 8.55521" width="41.2379pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.065,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.328,0)"><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,-0.013,25.568,0)"><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,-0.013,28.532,0)"><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,-0.013,34.772,0)"><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"></path></g></svg>,</span> after 345-time iteration, using the Cartesian discretization.</div>

International Journal of Differential Equations

fig15

Figure 15

Figure 15: A New Numerical Method to Solve Some <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3442pt" id="M1" height="15.5972pt" version="1.1" viewBox="-0.0657574 -11.253 37.2822 15.5972" width="37.2822pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g190-81" d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"/></g><g transform="matrix(.017,0,0,-0.017,9.575,0)"><path id="g190-69" d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"/></g><g transform="matrix(.017,0,0,-0.017,22.032,0)"><path id="g190-70" d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z"/></g><g transform="matrix(.012,0,0,-0.012,31.899,4.134)"><path id="g50-116" d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"/></g></svg> in the Unit Ball and Comparison with the Finite Element and the Exact Solution 

International Journal of Differential Equations

A New Numerical Method to Solve Some in the Unit Ball and Comparison with the Finite Element and the Exact Solution

Figure 15