article

Free access

An Automatic Program for Linear Fredholm Integral Equations of the Second Kind

Editor: John R. Rice Author:

Kendall AtkinsonAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 2, Issue 2

Pages 154 - 171

https://doi.org/10.1145/355681.355686

Published: 01 June 1976 Publication History

PDF eReader

References

[1]

ANSELONE, P.M. Colleetwely Compact Operator Approximation Theory. Prentice-Hall, Englewood Cliffs, N. j., 1971.

Google Scholar

[2]

ATKINSON, K.E. The numerical solution of Fredholm integral equations of the second kind. SIAM J. Numer. Anal. ~ (1967), 337-348.

Google Scholar

[3]

ATKINSON, K.E. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. SIAM Publ., Philadelphia, Pa. (SIAM Monograph), 1976.

Google Scholar

[4]

ATKINSON, K.E. Algorithm 503. An automatic program for Fredholm integral equations of the second kind. ACM Trans. Math. Software 2, 2 (June 1976), 196-199 (introductory comment listing only); complete listing m "Collected Algorithms from ACM," and also available from ACM Algorithms Distribution Service, Houston, Tex. 77036.

Crossref

Google Scholar

[5]

ATKINSON, K.E. Iterative variants of the Nystr(im method for the numerical solution of integral equations. Numer. Math. ~2 (1973), 17-31.

Google Scholar

[6]

ATKINSON, K.E. The numerical solution of Fredholm integral equations of the second kind with singular kernels. Numer. Math. 19 (1972), 248-259.

Google Scholar

[7]

BRAKHAGE, H. t~ber dm numensche Behandlung von Integralgleichungen nach der Quadraturformel methode. Numer. Math. 2 (1960), 183-196.

Google Scholar

[8]

DELVES, L.M. An automatic Ritz-Galerkm procedure for the numerical solution of hnear Fredholm integral equations of the second kind. Submitted for publication.

Google Scholar

[9]

DELVES, L.M., AND WALSH, J., EDS. Numerical Solutwn of Integral Equations. Clarendon Press, New York, 1974.

Google Scholar

[10]

ELLIOT, D., AND WARNS, W. An algorithm for the numerical solution of hnear integral equations. Int. Comput. Cent. Bull. 6 (1967), 207-224.

Google Scholar

[11]

NOBLE, B. A bibhography on methods for solving integral equations, author listing and subject hstmg. Tech. Reps. 1176 and 1177, Math. Res. Cent., U. of Wisconsin, Ma&son, Wls., 1971.

Google Scholar

[12]

RICE, J., ED., Mathematical Software. Academac Press (ACM Monograph Series), New York, 1971.

Crossref

Google Scholar

[13]

Riwsz, F., ANI) Sz.-NAQr, B. Functwnal Analysis, 2nd ed., translated by L.F. Boron. Ungar, New York, 1955.

Google Scholar

[14]

STROUD, A., AND SECRWST, D. Gaussian Quadrature Formulas. Prentice-Hall, Englewood Cliffs, N.J., 1966.

Google Scholar

Cited By

View all

Farina LLang GMartin P(2022)Love--Lieb Integral Equations: Applications, Theory, Approximations, and ComputationsSIAM Review10.1137/20M137103864:4(831-865)Online publication date: 3-Nov-2022
https://doi.org/10.1137/20M1371038
Seri R(2022)Computing the asymptotic distribution of second-order U- and V-statisticsComputational Statistics & Data Analysis10.1016/j.csda.2022.107437174:COnline publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1016/j.csda.2022.107437
Zhao JMa Y(2021)A Versatile Estimation Procedure Without Estimating the Nonignorable Missingness MechanismJournal of the American Statistical Association10.1080/01621459.2021.1893176117:540(1916-1930)Online publication date: 20-Apr-2021
https://doi.org/10.1080/01621459.2021.1893176
Show More Cited By

Index Terms

An Automatic Program for Linear Fredholm Integral Equations of the Second Kind
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Integral equations
    2. Numerical analysis
      1. Computations on matrices
  2. Mathematical software

Recommendations

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear ...
Numerical treatment of boundary value problems by solving a system of second kind Fredholm integral equations

A Nyström method is proposed for solving systems of Fredholm integral equations equivalent to special boundary value problems of order 2s . The stability and the convergence of the proposed procedure is proved. The GMRes method is applied to solve the ...
Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method

Using parametric form of fuzzy numbers we convert a linear fuzzy Fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case. We use Adomian method and find the approximate solution of this ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 2, Issue 2

June 1976

97 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/355681

Editor:
John R. Rice

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1976

Published in TOMS Volume 2, Issue 2

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

25
Total Citations
View Citations
1,137
Total Downloads

Downloads (Last 12 months)89
Downloads (Last 6 weeks)8

Reflects downloads up to 16 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Farina LLang GMartin P(2022)Love--Lieb Integral Equations: Applications, Theory, Approximations, and ComputationsSIAM Review10.1137/20M137103864:4(831-865)Online publication date: 3-Nov-2022
https://doi.org/10.1137/20M1371038
Seri R(2022)Computing the asymptotic distribution of second-order U- and V-statisticsComputational Statistics & Data Analysis10.1016/j.csda.2022.107437174:COnline publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1016/j.csda.2022.107437
Zhao JMa Y(2021)A Versatile Estimation Procedure Without Estimating the Nonignorable Missingness MechanismJournal of the American Statistical Association10.1080/01621459.2021.1893176117:540(1916-1930)Online publication date: 20-Apr-2021
https://doi.org/10.1080/01621459.2021.1893176
Brezinski CRedivo-Zaglia M(2019)Extrapolation methods for the numerical solution of nonlinear Fredholm integral equationsJournal of Integral Equations and Applications10.1216/JIE-2019-31-1-2931:1Online publication date: 1-Feb-2019
https://doi.org/10.1216/JIE-2019-31-1-29
MATUDA N(2015)Transmission Probability of Cylindrical Tubes —Eighty Years History of Clausing Equation—Journal of the Vacuum Society of Japan10.3131/jvsj2.58.31158:8(311-318)Online publication date: 2015
https://doi.org/10.3131/jvsj2.58.311
Atkinson KShampine L(2008)Algorithm 876ACM Transactions on Mathematical Software10.1145/1377596.137760134:4(1-20)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1145/1377596.1377601
Tang XPang ZZhu TLiu J(2007)Wavelet numerical solutions for weakly singular Fredholm integral equations of the second kindWuhan University Journal of Natural Sciences10.1007/s11859-006-0110-512:3(437-441)Online publication date: May-2007
https://doi.org/10.1007/s11859-006-0110-5
Micke AWendt W(2006)Über die Lösung von eindimensionalen Modellgleichungen des Ladungsträgertransportes in Halbleitern mit einer QuadraturformelmethodeZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik10.1002/zamm.1988068020668:2(79-87)Online publication date: 22-Nov-2006
https://doi.org/10.1002/zamm.19880680206
Lippold G(2006)Diskretisierungsfehler und Defektkorrekturen bei der Lösung von Gleichungen in Banach‐RäumenZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik10.1002/zamm.1980060100360:10(459-468)Online publication date: 23-Nov-2006
https://doi.org/10.1002/zamm.19800601003
Linton OMammen E(2005)Estimating Semiparametric ARCH(oo) Models by Kernel Smoothing Methods1Econometrica10.1111/j.1468-0262.2005.00596.x73:3(771-836)Online publication date: May-2005
https://doi.org/10.1111/j.1468-0262.2005.00596.x
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

Approximate solutions of Fredholm integral equations of the second kind

Numerical treatment of boundary value problems by solving a system of second kind Fredholm integral equations

Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations