Optimized Hybrid Methods for Solving Oscillatory Second Order Initial Value Problems

<div>The efficiency curves of the optimized and phase-fitted order five methods and their comparisons for Problem <a href="https://static-preview.hindawi.com/articles/ddns/volume-2015/217578/figures/#problem7">8</a> with <svg height="15.4868pt" id="M94" style="vertical-align:-3.4087pt" version="1.1" viewbox="-0.0498162 -12.0781 53.1495 15.4868" width="53.1495pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,4.552,3.264)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 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Discrete Dynamics in Nature and Society

fig7

Figure 7

Figure 7: Optimized Hybrid Methods for Solving Oscillatory Second Order Initial Value Problems 