Research Article

A Symmetric Quadrature Formula of Degree Nine for Analytic Functions

Abstract

A new novel quadrature rule of precision 9 is developed for integration of analytic functions. For development of new quadrature rule Taylor’s series plays a vital role. Richardson’s extrapolation has been used in improving the degree of precision of Boole’s precision from five to seven. Later the improved version of Boole’s rule is combined with another rule of precision seven to produce quadrature rule of precision 9 using Taylor’s expansion. In numerical computation four test examples has been adopted for investigating the efficiency of new quadrature rule and other classical quadrature rules. Approximated value, degree of precision and absolute error of newly developed quadrature rule along with other classical quadrature rules has been evaluated. It has been observed that the newly developed rule has less absolute error as compared to other rules which indicates that the new method is more efficient than the other methods. Also, absolute error of quadrature rules decreases with increase in degree of precision. Therefore, degree of precision varies inversely with absolute error of quadrature rules.