数值积分方法的比较教学研究与实验刘鹏飞.docx

Comparative teaching research and experiment of numerical integration methodLiu Pengfei, XU NainanAbstract: Numerical integration is a very important teaching content in the course of calculation method or numerical analysis. The numerical integration method is also an important method to solve practical problems.In this paper, we discuss the basic ideas of numerical integration method and some in the actual teaching comparative research and experiment teaching. Keywords:Numerical integration Calculation methodNumerical analysis Numerical experimentsText: The invention of calculus is a great achievement in the history of human science. However, in practical problems, there are still many limitations in solving integral. If the product function is often very complex, can not find the corresponding original function, or the product function is not a function expression, but in the form of a table, its original function is not meaningful.Therefore, it is significant to investigate the numerical integration method of approximate calculation.Basic ideas of numerical integration method By the integral mean value theorem, it is known that (x), b] (Qbaf) dx= (B-A) f (N) is set up in [a (x), which is a continuous function f (N). Problem is difficult to accurately calculate the average height of F (n) values, the different algorithms of F (n), you can get different numerical quadrature method, such as left (right) formula of rectangular, trapezoidal, Simpson formula. Generally, [a, b] some node XK at the height of F (XK) weighted average to approximate the average height of F (n), f (XK) linear combination to approximate the definite integral, mechanical quadrature formula: Qbaf(x)dxUEnk=0Akf(xk) Directly using the function computed values in the discrete node function integral, avoids the difficulty in seeking the original function, only need to be determined with the product function and product Ak quadrature coefficients are independent between partitions. In order to ens