An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation

<div>Temporal evolution with the initial states (14): (a) zero level contour of <svg height="12.7178pt" id="M171" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 46.1094 12.7178" width="46.1094pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.346,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.844,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 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Journal of Function Spaces

An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation

Figure 6