Numerical methods of integration.

*(English)*Zbl 0828.65014
Bromley: Chartwell-Bratt Ltd. 147 p. (1993).

This book, which describes many of the more recent and important techniques of numerical quadrature, was written mainly for undergraduates in mathematics and engineering. Some of the techniques however, would not be out of place in a more advanced post-graduate course in numerical quadrature.

The book itself is divided into nine chapters which describe Newton-Cotes quadrature, Gauss-type quadrature, Chebyshev polynomials, the error term arising from a quadrature rule, Kronrod quadrature, oscillatory/periodic integrands, integrands involving singularities and finally divergent integrals. Each chapter follows the same format of quoting relevant results illustrated by worked examples and followed by additional examples with supplied answers.

The author has included two appendices the first of which describes the Numerical Algorithms Group (NAG) Project whilst the second introduces the reader to sets of tables of global error bounds for most of the important quadrature rules. Until the appearance of such tables anyone wishing to approximate an integral by a numerical quadrature formula had, because of the error involved, to apply that formula at least twice. These tables allow the user to approximate an integral to any desired accuracy from just one application of the quadrature rule.

I have to appreciate the author’s access to the problem of giving widely chosen methods of numerical quadrature and a most suitable explanation of the problems arising in the studied field. The concept of the book is of full use for the students to whom it is dedicated.

The book itself is divided into nine chapters which describe Newton-Cotes quadrature, Gauss-type quadrature, Chebyshev polynomials, the error term arising from a quadrature rule, Kronrod quadrature, oscillatory/periodic integrands, integrands involving singularities and finally divergent integrals. Each chapter follows the same format of quoting relevant results illustrated by worked examples and followed by additional examples with supplied answers.

The author has included two appendices the first of which describes the Numerical Algorithms Group (NAG) Project whilst the second introduces the reader to sets of tables of global error bounds for most of the important quadrature rules. Until the appearance of such tables anyone wishing to approximate an integral by a numerical quadrature formula had, because of the error involved, to apply that formula at least twice. These tables allow the user to approximate an integral to any desired accuracy from just one application of the quadrature rule.

I have to appreciate the author’s access to the problem of giving widely chosen methods of numerical quadrature and a most suitable explanation of the problems arising in the studied field. The concept of the book is of full use for the students to whom it is dedicated.

Reviewer: J.Kofroň (Praha)

##### MSC:

65D32 | Numerical quadrature and cubature formulas |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

41-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and expansions |

41A55 | Approximate quadratures |

41A80 | Remainders in approximation formulas |

65A05 | Tables in numerical analysis |