Small Modification on Modified Euler Method for Solving Initial Value Problems

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"><span style="width: 7.39387ptpx;"><svg height="6.1673pt" id="M66" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.39387 6.1673" width="7.39387pt" 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="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></svg></span></td><td class="align_center" colspan="2">MEM</td><td class="align_center" colspan="2">IMEM</td><td class="align_center" colspan="2">Proposed method</td></tr><tr class="thead"><td class="align_center"><span style="width: 37.258ptpx;"><svg height="9.49473pt" id="M67" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 37.258 9.49473" width="37.258pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.34,0)"><path d="M535 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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,-0.013,37.047,0)"><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></span></td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">0.1</td><td class="align_center">1.110000</td><td class="align_center">1.1102531250</td><td class="align_center">1.11025000</td><td class="align_center">1.11032043066406</td><td class="align_center">1.11027750</td><td class="align_center">1.11032396426539</td></tr><tr><td class="align_left">0.2</td><td class="align_center">1.23105000</td><td class="align_center">1.24260943828613</td><td class="align_center">1.2426288125</td><td class="align_center">1.24276494414229</td><td class="align_center">1.24269248950625</td><td class="align_center">1.24277310856905</td></tr><tr><td class="align_left">0.3</td><td class="align_center">1.386810250</td><td class="align_center">1.39939257206320</td><td class="align_center">1.39946549501563</td><td class="align_center">1.39966082285240</td><td class="align_center">1.39957554807024</td><td class="align_center">1.39967490706942</td></tr><tr><td class="align_left">0.4</td><td class="align_center">1.56892532625</td><td class="align_center">1.58317043400224</td><td class="align_center">1.58333423836603</td><td class="align_center">1.58358016132462</td><td class="align_center">1.58350261283220</td><td class="align_center">1.58365746421514</td></tr><tr><td class="align_left">0.5</td><td class="align_center">1.78066248550625</td><td class="align_center">1.79678088708052</td><td class="align_center">1.79708016695405</td><td class="align_center">1.79736561854275</td><td class="align_center">1.79732080915464</td><td class="align_center">1.79745435154903</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Numerical solutions for Example <a href="https://static.hindawi.com/articles/aaa/volume-2021/9951815/figures/#ex2" target="_blank">2</a>.</div>

Abstract and Applied Analysis

tab3

Table 3

Table 3: Small Modification on Modified Euler Method for Solving Initial Value Problems 