On two methods for elimination of non-unique solutions of an integral equation with logarithmic kernel/Footnote^†

A Very short version of part of this paper bas been presented on April 18, 1979 at Scientific Meeting of “Gesellschaft für Angewandte Mathematik und Mechanik” (GAMM) [6].

References

• El-Seoud , M. S. Abou . 197 . Kollokationsmethode für schwach singuläre Integralgleichungen erster Art . Zeit, Angew. Math. Mech. (ZAMM) , 59 : T45 – T47 . (Sonderheft, GAMM-Tahung, Brussels 1978)
   Google Scholar
• El-Seoud , M. S. Abou . 1980 . Ein Vergleich von Kollokationsmethode und Galerkin-Verfahren für die numerische Lösung von schwach singulären Integralgleichungen erster Art . Zeit. Angew. Math. Mech. (ZAMM) , 60 : T278 – T280 . (Sonderheft, GAMM-Tagung, Wiesbaden 1979)
   Google Scholar
• Bauer , F. L. 1963 . Optimally scaled matrices . Numerische Mathematik , 5 : 73 – 87 .
   Google Scholar
• Christiansen , S. 1975 . Integral equations without a unique solution can be made useful for solving some plane harmonic problems . Jour. Inst. Math. Applications , 16 : 143 – 159 .
   Google Scholar
• Christiansen , S. and Rasmussen , H. 1976 . Numerical solutions for two-dimensional Annular electrochemical machining problems . Jour. Inst. Math. Applications , 18 : 295 – 307 .
   Google Scholar
• Christiansen , S. 1980 . How to suppress non-unique solutions to integral equations of the first kind . Zeit. Angew. Math. Mech. (ZAMM) , 60 : T244 – T245 . (Sonderheft, GAMM-Tagung, Wiesbaden 1979)
   Google Scholar
• Christiansen , S. 1980 . “ Numerical treatment of an integral equation originating from a two-dimensional Dirichlet boundary value problem ” . In Numerical Treatment of Integral Equations. , International Series of Numerical Mathematics. ISNM 53 Edited by: Albrecht , J. and Collatz , L. 275 – 275 . Boston, Stuttgart : Birkhaüser Verlag, Basel . Proceedings Oberwolfach Fed. Rep. Germany
   Google Scholar
• Christiansen S. 1982 In preparation
   Google Scholar
• Curtis , A. R. and Reid , J. K. 1972 . On the automatic scaling of matrices for Gaussian elimination . Jour. Inst. Math. Applications , 10 : 118 – 124 .
   Google Scholar
• Fletcher , T. J. 1972 . Linear Algebra Through its Applications , 10 – 274 . London : Van Nostrand Reinhold Company .
   Google Scholar
• Forsythe , G. E. and Moler , C. B. 1967 . Computer Solution of Linear Algebraic Systems , 11 – 148 . Englewood Cliffs : Prentice- Hall .
   Google Scholar
• Forsythe , G. E. , Malcolm , M. A. and Moler , C. B. 1977 . Computer Methods for Mathematical Computations , 11 – 259 . Englewood Cliffs : Prentice-Hall .
   Google Scholar
• Gradshteyn , I. S. and Ryzhik , I. M. 1965 . Table of Integrals, Series, and Products , 46 – 1086 . London, New York : Academic Press .
   Google Scholar
• Harrington , R. F. , Pontoppidan , K. , Abrahamsen , P. and Albertsen , N. C. 1969 . Computation of Laplacian potentials by an equivalent-source method . Proc. Instn. Elect. Engrs. , 116 : 1715 – 1720 .
   Google Scholar
• Hille , E. 1962 . Analytic Function Theory , Vol. 2 , 14 – 496 . Boston : Ginn and Company .
   Google Scholar
• Hsiao , G. and MacCamy , R. C. 1973 . Solution of boundary value problems by integral equations of the first kind . SIAM Review , 15 : 687 – 705 .
   Web of Science ®Google Scholar
• Hsiao , G. C. and Roach , G. F. 1979 . On the relationship between boundary value problems . Jour Math. Anal. Appl , 68 : 557 – 566 .
   Google Scholar
• Hsiao , G. C. , Kopp , P. and Wendland , W. L. 1980 . A Galerkin collocation method for some integral equations of the first kind . Computing , 25 : 89 – 130 .
   Google Scholar
• July 1977 . July , Houson, , U.S.A : IMSL Library 1 . (International Mathematical & Statistical Libraries Inc., 7500 Bellaire Blvd. Houston, Texas 77036, U.S.A.), LSVALR (singular value decomposition of a matrix)
   Google Scholar
• July 1977 . July , Houston, , U.S.A. : IMSL Library 1 . (International Mathematical & Statistical Libraries Inc., 7500 Bellaire Blvd. Houston, Texas 77036, U.S.A.), VSORTA (sort arrays by algebraic value)
   Google Scholar
• Jaswon , M. A. 1963 . Integral equation methods in potential theory . I Proc. Roy. Soc. London , A275 July : 23 – 32 .
   Google Scholar
• Jaswon , M. A. and Symm , G. T. 1977 . Integral Equation Methods in Potential Theory and Elastostatics , 14 – 287 . London, , San Francisco : Academic Press .
   Google Scholar
• Landkof , N. S. 1972 . Foundations of Modern Potential Theory , 10 – 424 . Berlin, Heidelberg, New York : Springer Verlag . (Die Grundlehren der mathematischen Wissenschaften, Band 180) (Translated from: Osnovy sovremennoi teorii potenciala, Nauka, Moscow 1966).
   Google Scholar
• Pólya , G. and Szegö , G. 1931 . Über den transfiniten Durchmesser (Kapazitätskonstante) von ebenen und räumlichen Punktmengen . Jour. Reine Angew. Math. , 165 : 4 – 49 .
   Google Scholar
• Pólya , G. and Szegö , G. 1951 . Isoperimetric Inequalities in Mathematical Physics , 15 – 279 . Princeton : Princeton University Press . [Annals of Mathematics Studies, No. 27].
   Google Scholar
• Symm , G. T. 1963 . Integral equation methods in potential theory . II, Proc. Roy. Soc. London , A275 : 33 – 46 .
   Google Scholar
• Symm , G. T. 1969 . Condition numbers and equilibration of matrices . Numerische Mathematik , 14 : 14 – 23 .
   Google Scholar
• Symm , G. T. 1970 . Numerische Mathematik , 15 : 74 – 86 .
   Google Scholar