The Construction and Asymptotic Behavior of a High-precision Trapezoidal Correction Formula

Based on a low order trapezoidal formula, using the concept of algebraic accuracy in numerical integration formulas to determine the quadrature coefficients, a new trapezoidal correction formula with algebraic accuracy of degree five is constructed, and the expression of remainder is obtained. Finally, the asymptotic property of the intermediate value point of the remainder is discussed.