Introduction to Numerical Analysis and Scientific Computing

Chapter 6

Advanced Numerical Integration

6.1Numerical Integration for Non-Uniform Partitions

6.1.1Generalized Formulae and Error Analysis

6.1.2The Case for Adaptive Numerical Integration

6.1.3Adaptive Simpson’s Integration

6.2Numerical Integration of Functions of Two Variables

6.2.1Double Integrals over Rectangular Domains

6.2.2Double Rectangular Rule

6.2.3Double Trapezoidal and Midpoint Rules

6.2.4Double Simpson’s Rule

6.2.5Error Estimates

6.2.6Double Integrals over Convex Polygonal Domains

6.3Monte Carlo Simulations for Numerical Quadrature

6.3.1On Random Number Generation

6.3.2Estimation of Integrals through Areas and Volumes

6.3.3Estimating Mean Values

6.4Exercises

6.5Computer Exercises

6.1 Numerical Integration for Non-Uniform Partitions ...