Some Applications For High Accuracy Algorithm

This article has emphatically studied two kinds of high accuracy algorithm of the numerical value analysis: extrapolation and corrector method, the application was the following aspects.1. The numerical integration fundemental formulas were summaried; It was discussed emphatically that the low step Gauss quadrature formula and the asymptotic expansion of trapezoid quadrature formula, and obtained the corresponding formula of extrapolation and corrector, thus, obtained the numerical integration formula of high accuracy.2. On the basis of integral high accuracy, further discussed the numerical value solution of integral equation—distribution point and Galerkin, after strict theoretical derivation, and got the corresponding asympototic expansion formula, obtained high accuracy algorithm of integral equation—extrapolation and corrector formula.3. Futher studied the calculus of finite differences of one-dimensional second order clliptic boundary value problems.