Research On Several Problems Of The Numerical Integration

The numerical calculation of integration is an important branch of numerical analysis. It is derived by the origins of numerical approximation integration and introduces some important methods of numerical integration in detail in the dissertation.Under the one-dimensional situation, it introduces mainly the Newton-Cotes formula, the Gaussian quadrature formula, the numerical integration rule of sharp oscillatory function, the numerical integration rule by the methods of sampling and so on. The author of this text has put out a kind of new-type quadrature formula by using the Gaussian quadrature formula and the orthogonality of Per Kai polynomial. The integration rule is simple because of the convenience of the integral nodes.Under the higher-dimensional situation, it introduces mainly the multiple integrals formulas on some standard areas, the multiple integrals formula by the methods of sampling, the reduction of dimensions and the boundary type cubature with a certain algebraic precision, and calculate multiple integrals with the methods of number theoretical net and so on. The author of this text make the Cotes formula extend for n-dimensional space through fine nature of higher-dimensional rectangular region. And the more convient truncation error estimation is made.