An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation

<div>Snapshots of the numerical solutions of the Fisher–KPP equation with the initial condition <span class="nowrap"><svg height="11.5564pt" id="M172" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 153.297 11.5564" width="153.297pt" 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="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.994,0)"><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 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Discrete Dynamics in Nature and Society

fig10

Figure 10

Figure 10: An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation 