numerical integration

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11: 3.5 Quadrature

§3.5 Quadrature

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§3.5(ix) Other Contour Integrals

… ►A special case is the rule for Hilbert transforms (§1.14(v)): …

12: Bibliography D

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Methods of Numerical Integration. 2nd edition, Computer Science and Applied Mathematics, Academic Press Inc., Orlando, FL.

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External Links:

ISBN 0-12-206360-0, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§3.5(iii), §3.5(i), §3.5(i), §3.5(ii), §3.5(iii), §3.5(iv), §3.5(v), §3.5(vi), §3.5(vii), §3.5(x).

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13: Philip J. Davis

… ►Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky. …

14: Bibliography M

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Notes:

Mpmath is a pure-Python library for multiprecision floating-point arithmetic. It provides an extensive set of transcendental functions, unlimited exponent sizes, complex numbers, interval arithmetic, numerical integration and differentiation, root-finding, linear algebra, and much more.

External Links:

mpmath

Referenced by:

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15: 9.17 Methods of Computation

… ►A comprehensive and powerful approach is to integrate the defining differential equation (9.2.1) by direct numerical methods. …

16: 11.13 Methods of Computation

… ►A comprehensive approach is to integrate the defining inhomogeneous differential equations (11.2.7) and (11.2.9) numerically, using methods described in §3.7. …

17: Bibliography H

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Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems. Ph.D. Thesis, Technischen Universität Berlin.

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Notes:

(All relevant material, plus corrections, are included in Deconinck et al. (2004).)

External Links:

ZentralBlatt

Referenced by:

§21.5(i).

Encodings:

BibTeX

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18: 36.15 Methods of Computation

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§36.15(iii) Integration along Deformed Contour

►Direct numerical evaluation can be carried out along a contour that runs along the segment of the real $t$-axis containing all real critical points of $\mathrm{\Phi }$ and is deformed outside this range so as to reach infinity along the asymptotic valleys of $\exp \left(\mathrm{i}\mathrm{\Phi }\right)$. … ►

§36.15(iv) Integration along Finite Contour

►This can be carried out by direct numerical evaluation of canonical integrals along a finite segment of the real axis including all real critical points of $\mathrm{\Phi }$, with contributions from the contour outside this range approximated by the first terms of an asymptotic series associated with the endpoints. … ►For numerical solution of partial differential equations satisfied by the canonical integrals see Connor et al. (1983).

19: Bibliography S

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NUMER, a code for Numerov integrations of Coulomb functions. Comput. Phys. Comm. 146 (2), pp. 254–260.

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Notes:

Single-precision Fortran code.

External Links:

Document, Code, ZentralBlatt

Referenced by:

11st item.

Encodings:

BibTeX

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20: 10.74 Methods of Computation

… ►A comprehensive and powerful approach is to integrate the differential equations (10.2.1) and (10.25.1) by direct numerical methods. …