Reliable Computing of Definite Integrals Based on Interval Analysis
This paper mainly studies the reliable computing of definite integral,that is,based on interval inclusion theorem,with the help of professional interval arithmetic software to construct algorithm programs to rigorously compute interval enclosures of the definite integral values.Firstly,the interval polynomial enclosure of the integrand on the integration interval is given by using Taylor's formula,inclusion isotonicity of interval function and interval arithmetic operators;Then,the mathematical formula for computing the inclusion interval of definite integral value is constructed by using the interval integral theory,which is composed of two polynomial integrals with the same integral interval,and can calculate the interval enclosure of arbitrarily narrow width;Finally,according to the formula,an algorithm program for practical computation is designed by using the interval operation software that performs outward rounding.Theoretical analysis and numerical experiments illustrate the performance of the proposed algorithm.