An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation

<div><span class="nowrap"><svg height="11.439pt" id="M286" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 39.4241 11.439" width="39.4241pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path></g><g transform="matrix(.013,0,0,-0.013,10.107,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,21.37,0)"><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></g><g transform="matrix(.013,0,0,-0.013,27.61,0)"><path d="M368 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541 160Z" id="g113-77"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> errors for the NSFD scheme (<a href="https://static.hindawi.com/articles/amp/volume-2017/4796070/figures/#EEq10">10</a>), and standard scheme (<a href="https://static.hindawi.com/articles/amp/volume-2017/4796070/figures/#EEq11">11</a>): <span class="nowrap"><svg height="8.8423pt" id="M289" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 46.1833 8.8423" width="46.1833pt" 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="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z" 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Advances in Mathematical Physics

fig3

Figure 3

Figure 3: An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation 