aiming at the problems of slow convergence speed and insufficient node utilization of the double trapezoidal recursion algorithm, a method with higher accuracy and faster convergence of the algorithm—double simpson recursion algorithm is proposed, from which the double simpson recursion formula of double integration is halved in the interval under a rectangular region, and the specific algorithm implementation is given. the algorithm is applied to calculate the double integration problem of continuous functions under rectangular region and irregular region, respectively. by calculating the area of the upper semi-ellipsoidal surface, it is concluded that the double simpson recursion algorithm has faster convergence speed, higher calculation accuracy and shorter program calculation time than the double trapezoidal recursion algorithm. finally, by solving the initial value problem of the chord vibration equation, the application of the double simpson recursion algorithm in the double integral calculation under the general integration region is given, which shows that the applicability of the double simpson recursion algorithm is stronger, and the application of the algorithm in the field of partial differential equations is further explained.