Construction Of Two-dimensional Numerical Integration Formula Methods

Numerical integration is an important branch of computational mathematics. Numerical integration of one-dimensional case has been studied for many years in engineering technology increasingly developed modern, two-dimensional and multi-dimensional integration is vitally important to the numerical calculation. This paper is an important method of numerical integration, equidistant nodes method, combined with one-dimensional structure of Quadrature people thought, in two-dimensional space is extended, constructed a number of two-dimensional quadrature formula.The article is divided in five parts; the first part is the foundation of knowledge, first introduced the basic concepts of numerical integration, as well as previous one-dimensional numerical integration of the important part - Equidistant quadrature methods described induction. Part II and Part III in a dimensional space, based on two dimensional space at the basic unit - Triangular and rectangular fields, the idea of incremental progress in trying to construct quadrature formula, the formula of the construction process and led to all the thinking. The fourth part will be the second and third part of the quadrature formula range complex in order to improve their accuracy and reduce errors. Numerical experiments were also conducted on different quadrature formulas were compared. Part V summarizes the construction of high-dimensional integral formula ideological principles. Integral Quadrature and integral function of the region itself, the complexity, uncertainty, so as the dimension increases, the classical one-dimensional numerical integration is very difficult to directly extended to high dimension, so that it becomes very difficult to study. Therefore, a correct formula for the construction of numerical integration methods is essential. This numerical integration process by constructing a summary, which has a very deep experience.