基于拓展的倍增法的无穷限广义积分数值计算分析与研究

The Analysis and Research of Infinite Generalized Integral Numerical Calculation Based on the Extended Method of Multiplication

为了解决复杂函数的无穷限广义积分无法通过分步积分法得到精确结果的问题,科研工作者提出了以数值逼近的方法去求解该类积分的近似数值解,用该数值解去替代原广义积分。在实际应用中发现,此方法存在潜在的悖论问题。针对该问题,提出将倍增法应用到无穷限广义积分的数值求解中。通过将倍增法进行有针对性地拓展,从而既解决了潜在的悖论问题,又提升了数值计算速度与稳定性。从而为无穷限广义积分在计算数学、应用数学、经济学等学科中的更进一步推广打下了坚实的基础。

In order to solve the complex functions of infinite integrals by step-by-step integration method can get accurate results, researchers put forward with numerical approximation method to solve the integral approximate numerical solu- tion, the numerical solution to replace the original generalized integral. In practical application, this method has potential paradox. Aiming at this problem, the multiplier method is applied to the infinite generalized integral numerical solution. The multiplication method for targeted development, which not only resolves potential paradox, and improve the speed and stability of numerical calculation. Thus for infinite generalized integral in computational mathematics, applied mathe- matics, economics and other disciplines in the further promotion and lay a solid foundation.