Runge-Kutta scheme is one of the versatile numerical tools for the simulation of engineering systems. Despite its wide and acceptable engineering use, there is dearth of relevant literature bordering on visual impress...Runge-Kutta scheme is one of the versatile numerical tools for the simulation of engineering systems. Despite its wide and acceptable engineering use, there is dearth of relevant literature bordering on visual impression possibility among different schemes coefficients which is the strong motivation for the present investigation of the third and fourth order schemes. The present study capitalise on results of tedious computation involving Taylor series expansion equivalent supplemented with Butcher assumptions and constraint equations of well-known works which captures the essential relationship between the coefficients. The simulation proceeds from random but valid specification of two out of the total coefficients possible per scheme. However the remaining coefficients are evaluated with application of appropriate function relationship. Eight and thirteen unknown coefficients were simulated respectively for third and fourth schemes over a total of five thousand cases each for relevant distribution statistics and scatter plots analysis for the purpose of scheme comparison and visual import. The respective three and four coefficients of the slope estimate for the third and fourth schemes have mix sign for large number of simulated cases. However, none of the two schemes have above three of these coefficients lesser than zero. The percentages of simulation results with two coefficients lesser than zero dominate and are respectively 56.88 and 77.10 for third and fourth schemes. It was observed that both popular third and fourth schemes belong to none of the coefficients being zero classification with respective percentage of 0.72 and 3.28 intotal simulated cases. The comparisons of corresponding scatter plots are visually exciting. The overall difference between corresponding scatter plots and distribution results can be used to justify the accuracy of fourth scheme over its counterpart third scheme.展开更多
目的:基于文献计量学分析榄香烯相关研究领域的发展现状和发展态势。方法:从中国知网(CNKI)和Web of Science核心合集中检索2004—2024年榄香烯研究领域的相关文献,运用CiteSpace和VOSviewer进行文献计量学与可视化分析。结果:共纳入文...目的:基于文献计量学分析榄香烯相关研究领域的发展现状和发展态势。方法:从中国知网(CNKI)和Web of Science核心合集中检索2004—2024年榄香烯研究领域的相关文献,运用CiteSpace和VOSviewer进行文献计量学与可视化分析。结果:共纳入文献1 821篇,其中中文文献462篇,英文文献1 359篇。相比之下,英文文献发文量较大且总体呈逐年上升趋势。中英文发文量均为第一的作者为杭州师范大学的谢恬,其所在单位杭州师范大学也是英文文献发文量第一的科研机构。中英文关键词显示,榄香烯的研究热点主要集中于活性成分分析、榄香烯衍生产品和抗肿瘤作用。主要成分“β-榄香烯”为中英文文献中出现频数最高的关键词。结论:榄香烯相关研究领域目前仍处于上升阶段,发展前景良好,因此应深度剖析榄香烯的可能作用机制和临床应用,充分发挥其疗效优势和临床价值以推动中医药的传承创新发展。展开更多
文摘Runge-Kutta scheme is one of the versatile numerical tools for the simulation of engineering systems. Despite its wide and acceptable engineering use, there is dearth of relevant literature bordering on visual impression possibility among different schemes coefficients which is the strong motivation for the present investigation of the third and fourth order schemes. The present study capitalise on results of tedious computation involving Taylor series expansion equivalent supplemented with Butcher assumptions and constraint equations of well-known works which captures the essential relationship between the coefficients. The simulation proceeds from random but valid specification of two out of the total coefficients possible per scheme. However the remaining coefficients are evaluated with application of appropriate function relationship. Eight and thirteen unknown coefficients were simulated respectively for third and fourth schemes over a total of five thousand cases each for relevant distribution statistics and scatter plots analysis for the purpose of scheme comparison and visual import. The respective three and four coefficients of the slope estimate for the third and fourth schemes have mix sign for large number of simulated cases. However, none of the two schemes have above three of these coefficients lesser than zero. The percentages of simulation results with two coefficients lesser than zero dominate and are respectively 56.88 and 77.10 for third and fourth schemes. It was observed that both popular third and fourth schemes belong to none of the coefficients being zero classification with respective percentage of 0.72 and 3.28 intotal simulated cases. The comparisons of corresponding scatter plots are visually exciting. The overall difference between corresponding scatter plots and distribution results can be used to justify the accuracy of fourth scheme over its counterpart third scheme.
文摘目的:基于文献计量学分析榄香烯相关研究领域的发展现状和发展态势。方法:从中国知网(CNKI)和Web of Science核心合集中检索2004—2024年榄香烯研究领域的相关文献,运用CiteSpace和VOSviewer进行文献计量学与可视化分析。结果:共纳入文献1 821篇,其中中文文献462篇,英文文献1 359篇。相比之下,英文文献发文量较大且总体呈逐年上升趋势。中英文发文量均为第一的作者为杭州师范大学的谢恬,其所在单位杭州师范大学也是英文文献发文量第一的科研机构。中英文关键词显示,榄香烯的研究热点主要集中于活性成分分析、榄香烯衍生产品和抗肿瘤作用。主要成分“β-榄香烯”为中英文文献中出现频数最高的关键词。结论:榄香烯相关研究领域目前仍处于上升阶段,发展前景良好,因此应深度剖析榄香烯的可能作用机制和临床应用,充分发挥其疗效优势和临床价值以推动中医药的传承创新发展。
