One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static-preview.hindawi.com/articles/jam/volume-2024/5078943/figures/5078943.fig.007a.svgz" name="5078943.fig.007a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Solution profile of <svg height="9.39034pt" id="M363" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 12.0141 9.39034" width="12.0141pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static-preview.hindawi.com/articles/jam/volume-2024/5078943/figures/5078943.fig.007b.svgz" name="5078943.fig.007b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Solution profile of <svg height="9.39034pt" id="M364" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 12.0141 9.39034" width="12.0141pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><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"></path></g></svg></td></tr></table>

<div>Solution profile of Example <a href="https://static-preview.hindawi.com/articles/jam/volume-2024/5078943/figures/#ex4">4</a> with NMm1.</div>

Journal of Applied Mathematics

fig7

Figure 7

Figure 7: One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems 