Errors in Numerical Quadrature Schemes, 1998
Wilson, Joycelyn N.
1990-1999
As a general rule, it is not possible to express the integral, ?abf(x)dx, of a real valued function f of a single real variable x, in terms of relatively elementary functions. Even when this can be done, numerical calculations based on such expressions may be lengthy and tedious. For these reasons, mathematicians have devised several numerical quadrature schemes to provide approximate values for the integral (1). The error in any such scheme is defined as the difference between the integral and the numerical quadrature scheme. In this paper, we studied the errors in four specific numerical quadrature schemes: trapezoidal rule, midpoint rule, Simpsons rule, and Bodes rule. Our interest was to find estimates for these errors. The approach was first to find an explicit formula for the error. This formula involved an integral, one factor of whose integrand was a derivative of some order of the function f(x). Both upper and lower bounds were found for the error in terms of the maximum and minimum values of that derivative. Numerical results were finally calculated for two specific functions f(x). We found that Bodes rule gave the most accurate answer while the trapezoidal rule was least accurate.
text
application/pdf
1998-05-01
thesis
Master of Science (MS)
Clark Atlanta University
School of Arts and Sciences, Mathematical Sciences
Wilkins, J. Ernest
Georgia--Atlanta
http://hdl.handle.net/20.500.12322/cau.td:1998_wilson_joycelyn_n
