一种任意重积分自适应递归式快速计算方法

An Adaptive Recursive Fast Method for Arbitrary Multiple Integral

当前一些科学计算软件虽然能够利用数值积分得到复杂积分的近似解,但最多只能求解三重积分。为解决积分计算重数受限问题,基于累次积分的解析计算思路,结合递归算法,提出了一种任意重积分自适应递归式快速计算方法。从原理上介绍了算法思路和递归过程,给出了在MATLAB中运行的算法源程序代码。在算例和工程应用上,将该方法与现有方法进行了对比。结果表明了该方法的有效性,可使计算时间大大缩短,只需提供积分区间和被积函数即可求解,省去了将程序代码与积分重数进行匹配的编程步骤。方法操作简单,计算精度高,速度快,可满足实际工程需要。

At present,some scientific calculation software can get approximate solution of complex integration through numerical integration.However,scientific calculation software can only solve triple integration at most.To solve the problem of limited multiplicity in integral calculation,an adaptive recursive fast calculation method for arbitrary multiple integrals was proposed.It was based on the analytic calculation idea of multiple integrals and recursive algorithm.The algorithm and recursion process of the method were introduced in principle,and the source code of the method was given in MATLAB.The method was compared with the existing methods by examples.The results indicate the effectiveness of the proposed method.This method can reduce the calculation time greatly.It can be solved only by providing integral interval and integrand function,eliminating the programming steps of matching program code with integral multiplicity.The method is simple in operation,and high in calculation accuracy and speed,which can meet the actual engineering needs.