中文摘要：

将宋代最具代表性的历法《纪元历》的日食预报方法公式化,并完全按照《纪元历》推算方法编写计算机程序,利用程序计算了宋代的全部日食,并与现代计算结果进行了比较分析.结果表明,《纪元历》推算日食的精度是：食甚的最大误差为1.2588小时,平均误差为0.4033小时；食分的最大误差为6.2分,平均误差为1.3分.结合《纪元历》推算定朔的精度,得出其时差的计算精度在0.5小时以上,这个值比重建模型估算值稍大一些.最后指出虽然《纪元历》日食算法的方法不够优化,且时差精度较低,但就日食的最终推算结果来看,其日食数值算法系统仍是很合理的和有效的.

英文摘要：

Jiyuan Li is the most representative calendar in Song dynasty. The computation process of solar eclipse in Jiyuan Li is reconstructed and a computer program of such a computation is compiled. This paper calculates all solar eclipses from AD 960 to 1276 in Song dynasty using the methods of Jiyuan Li. Comparing these calculations with modern values, the paper estimates the ac- curacy of the calendar. The results are as follows： the biggest error of middle of eclipse is 1. 2588 hours and the average error is 0. 4033 hours. The maximum error of the magnitude of eclipse is 6.2 and the average error is 1.3. Based on the calculation for its accuracy of the real new noon, the aver- age error of shicha can be obtained. It is about 0.5 hours and is bigger than the theoretical result. Finally, the paper points out that the calculation on solar eclipse is not optimization and the precision of equation of time is low. However, considering of the final results of calculation of solar eclipse, the numerical algorithm system of eclipse is still very reasonable and excellent.