21 - Numerical Integration

Abstract

This chapter focuses on the numerical integration. The chapter reviews the open- and closed-type formulas. An integration formula is said to be of the closed type if it requires the function values to be determined at the end points of the interval of integration, so that x0= a and xn = b. An integration formula is said to be of open type if x0 >a and xn < b. Many fundamental numerical integration formulas are based on the assumption that an interval of integration contains a specified number of abscissas at which points the function must be evaluated. Thus, in the basic Simpson's rule, the interval a ≤ x ≤ b is divided into two subintervals of equal length at the ends of which the function has to be evaluated, so that f(x0), f(x1), and f(x2) are required, with x0 = a, x1 = ½(a + b), and x2 = b.