Overview

1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi­ cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as orthogo­ nal polynomials, Fourier series and number theory have had important implications for the evaluation of integrals. We denote the problem addressed here as numerical integration or numerical quadrature. Over the years analysts and engineers have contributed to a growing body of theorems, algorithms and lately, programs, for the solution of this specific problem. Much effort has been devoted to techniques for the analytic evalua­ tion of integrals. However, most routine integrals in practical scien­ tific work are incapable of being evaluated in closed form. Even if an expression can be derived for the value of an integral, often this reveals itself only after inordinate amounts of error prone algebraic manipulation. Recently some computer procedures have been developed which can perform analytic integration when it is possible.

Full Product Details

Author:   R. Piessens ,  E. de Doncker-Kapenga ,  C.W. Überhuber ,  D.K. Kahaner
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1983
Volume:   1
Dimensions:   Width: 15.20cm , Height: 1.60cm , Length: 22.90cm
Weight:   0.465kg
ISBN:  

9783540125532

ISBN 10:   3540125531
Pages:   304
Publication Date:   01 July 1983
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

I. Introduction.- II. Theoretical Background.- 2.1. Automatic integration with QUADPACK.- 2.2. Integration methods.- 2.2.1. Quadrature sum.- 2.2.2. Construction of Gauss-type rules with preassigned abscissae.- 2.2.3. Modified Clenshaw-Curtis integration.- 2.2.4. Numerical quadrature and extrapolation.- III. Algorithm Descriptions.- 3.1. QUADPACK contents.- 3.2. Prototype of algorithm description.- 3.3. Algorithm schemes.- 3.4. Heuristics used in the algorithms.- IV. Guidelines for the use of Quadpack.- 4.1. General remarks.- 4.2. Decision tree for finite-range integration.- 4.3. Decision tree for infinite-range integration.- 4.4. Numerical examples.- 4.5. Sample programs illustrating the use of the QUADPACK integrators.- V. Special Applications of Quadpack.- 5.1. Two-dimensional integration.- 5.2. Hankel transform.- 5.3. Numerical inversion of the Laplace transform.- VI. Implementation Notes and Routine Listings.- 6.1. Implementation notes.- 6.2. Routine listings.- QNG.- QAG.- QAGE.- GAGS.- QAGP.- QAGI.- QAWO.- QAWF.- QAWFE.- QAWS.- QAWSE.- QAWC.- QAWCE.- QFOUR.- QK15.- QK21.- QK31.- QK41.- QK51.- QK61.- QK15I.- QK15W.- QEXT.- QSORT.- QC250.- QC25S.- QC25C.- QMOMO.- QCHEB.- QWGTO.- QWGTS.- QWGTC 29.- QMACO.- References.

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