关键词: 子午线弧长, 数值积分, 常微分方程, 展开算法

Abstract: There are several kinds of algorithms for calculating the meridian arc length except the classical expanded algorithm, such as numerical integration and ordinary differential equations numerical solution. In order to study the accuracy of each algorithm, this paper selected 3 sets of sample data within the geodetic latitude from 0° to 90°, whose intervals are 1°,1',1″, respectively. Based on the traditional expanded algorithms, numerical integral algorithms and numerical solution of ordinary differential equations, the corresponding meridian arc length results were calculated and the quality of each numerical algorithm with regard to algorithm accuracy and computation speed were evaluated. The results show that the 3 and 4 order Runge-Kutta algorithm not only have high precision but the computing speed is twice more than other algorithms. This paper provides new, reliable algorithm with high speed for meridian arc length calculation. The results provide an effective algorithm for calculating the meridian arc length.

Key words: meridian arc length, numerical integral, ordinary differential equations, expanded algorithm