Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly

<table>Graph of <svg height="13.8414pt" id="M337" style="vertical-align:-4.1635pt" version="1.1" viewbox="-0.0498162 -9.6779 78.15 13.8414" width="78.15pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z" id="g190-77"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="538" vert-adv-y="538"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.411,0)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g190-112"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="510" vert-adv-y="510"></glyph.data></g><g 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-63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg> plotted against <svg height="13.8414pt" id="M338" style="vertical-align:-4.1635pt" version="1.1" viewbox="-0.0498162 -9.6779 51.4416 13.8414" width="51.4416pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z" id="g190-77"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="538" vert-adv-y="538"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.411,0)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 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descent="-360" horiz-adv-x="468" vert-adv-y="468"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,20.738,3.999)"><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" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,25.357,3.999)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,30.508,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,35.196,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z" id="g113-73"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="840" vert-adv-y="840"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,46.58,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg> for Problem 1.</table>

Abstract and Applied Analysis

fig2

Figure 2

Figure 2: Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly 