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Numerical Quadrature and Solution of Ordinary Differential Equations pp 106–205Cite as

Quadrature

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Part of the book series: Applied Mathematical Sciences ((AMS,volume 10))

Abstract

In this chapter we discuss methods for approximating definite integrals. Most of the approximations we discuss have the general form

$$ \int_a^b {w(x)f(x)dx} = {A_1}f\left( {{x_1}} \right) + {A_2}f\left( {{x_2}} \right) + ... + {A_n}f\left( {{x_n}} \right) + E\left[ f \right] $$
((1))

We call such approximations quadrature formulas or integration formulas. The xk are called the points (or nodes) in the formula; the Ak are called the coefficients (or weights) in the formula. E[f] is the error in the approximation.

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Authors and Affiliations

  1. Department of Mathematics, Texas A & M University, USA

    A. H. Stroud

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  1. A. H. Stroud
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© 1974 Springer-Verlag New York Inc.

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Stroud, A.H. (1974). Quadrature. In: Numerical Quadrature and Solution of Ordinary Differential Equations. Applied Mathematical Sciences, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6390-6_3

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  • DOI: https://doi.org/10.1007/978-1-4612-6390-6_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90100-8

  • Online ISBN: 978-1-4612-6390-6

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