数值积分算法与MATLAB实现研究--重庆邮电大学本科毕业论文

The undergraduate thesis "Numerical Integration Algorithm and MATLAB Implementation" explores the efficient methods of numerical integration for calculating approximations of definite integrals when the original functions are too complex to be expressed using elementary functions. Due to the difficulty in finding exact solutions for these integrals, numerical integration provides a practical approach to obtaining accurate approximations. The study begins by discussing the significance of numerical integration in the field of numerical analysis and the various methods used for approximating integrals. The thesis extensively covers the Newton-Cotes quadrature formula, as well as higher-precision numerical integration formulas such as the Romberg integration formula and the Gauss-Legendre quadrature formula. In addition to examining the theoretical aspects of these numerical integration algorithms, the study also presents the implementation of these algorithms through programming in MATLAB software. By utilizing various integration formulas on practical examples, the study compares and analyzes the computational errors produced by each method. Through the thorough investigation of numerical integration algorithms and their implementation in MATLAB, this study provides valuable insights into the practical applications of numerical integration for solving complex integrals. The comparison of different integration formulas and their computational accuracies contributes to a better understanding of the efficiency and reliability of these numerical methods. The findings presented in this thesis offer useful information for researchers and practitioners in the field of numerical analysis and computational mathematics.