【摘要】：計(jì)算子午線弧長(zhǎng)除了采用經(jīng)典的級(jí)數(shù)展開(kāi)算法之外,還可通過(guò)數(shù)值積分與常微分方程數(shù)值解法進(jìn)行求解。為評(píng)價(jià)各種算法的精度,本文選取大地緯度自0°—90°、間隔距離為1°、1'、1″的3組樣本數(shù)據(jù),分別基于傳統(tǒng)算法、數(shù)值積分算法和常微分方程數(shù)值算法3大類11種算法計(jì)算得到各組樣本所對(duì)應(yīng)的子午線弧長(zhǎng)結(jié)果,并從算法精度和運(yùn)算速度兩個(gè)方面對(duì)各種數(shù)值算法進(jìn)行了分析與評(píng)價(jià)。實(shí)例表明三階、四階Runge-Kutta算法不僅精度高,而且運(yùn)算效率是其他算法的2倍多,研究結(jié)果為計(jì)算子午線弧長(zhǎng)的提供了有效的算法模型。
[Abstract]:In addition to the classical series expansion algorithm, the meridian arc length can also be solved by numerical integration and numerical solution of ordinary differential equations. In order to evaluate the accuracy of various algorithms, this paper selects three sets of sample data with latitude from 0 擄to 90 擄and interval distance of 1 擄, 1 擄and 1 ", respectively, based on the traditional algorithm. Numerical integration algorithm and ordinary differential equation numerical algorithm are used to calculate the meridian arc length corresponding to each sample, and the accuracy and speed of the algorithm are analyzed and evaluated. The example shows that the third-order and fourth-order Runge-Kutta algorithms are not only accurate, but also more than twice as efficient as other algorithms. The research results provide an effective algorithm model for calculating meridian arc length.
【作者單位】： 河南省中緯測(cè)繪規(guī)劃信息工程有限公司;鄭州工業(yè)貿(mào)易學(xué)校;
【基金】：2016年國(guó)家重點(diǎn)研發(fā)計(jì)劃(2016YFC0803103) 河南省高校創(chuàng)新團(tuán)隊(duì)支持計(jì)劃(14IRTSTHN026) 河南省創(chuàng)新型科技創(chuàng)新團(tuán)隊(duì)支持計(jì)劃
【分類號(hào)】：P226

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