We transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (1e-15). We also use the algorithm to determine the error curve for a Simpson cubature rule.

翻译：我们将双重积分转化为一个二阶初值问题，并采用欧拉法和理查森外推法进行求解。针对所考察的算例，我们实现了接近机器精度（1e-15）的计算精度。该算法还可用于确定辛普森立方体求积规则的误差曲线。