基于蛙跳算法求任意函数的数值积分

Solving Numerical Integration Based on Shuffled Frog Leaping Algorithm

针对复杂函数的数值积分问题,给出了若干个任意分割积分区间的数值积分的误差结果,提出一种基于蛙跳算法的不等距节点分割的数值积分方法。该方法初始时在积分区间内任意选取一定的节点,通过蛙跳算法优化这些节点,在相邻节点间利用Simpson公式近似计算积分,最后得到较准确的积分结果。数值计算结果表明,该方法计算精度高,而且可以高效处理不存在初等原函数以及复杂的有理函数的积分。

In this paper several numerical integral error results based on subdividing the integral interval arbitrarily is presented, then an approach for solving numerical integration based on Shuffled Frog Leaping Algorithm（SFLA） is proposed. SFLA is used to optimize the points in the integral interval in order to get a more precise result with using Simpson＇ s Rule in every small segment. Simulation examples of integral validate the algorithm that can compute both complicated function integral which haven＇t elementary anti-derivative function and rational function integral.