{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:25:00Z","timestamp":1753921500145},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1985,9,1]],"date-time":"1985-09-01T00:00:00Z","timestamp":494380800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1985,9]]},"DOI":"10.1007\/bf02253319","type":"journal-article","created":{"date-parts":[[2005,11,22]],"date-time":"2005-11-22T14:43:09Z","timestamp":1132670589000},"page":"221-242","source":"Crossref","is-referenced-by-count":6,"title":["Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning"],"prefix":"10.1007","volume":"34","author":[{"given":"S.","family":"Christiansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02253319_CR1","unstructured":"Abou El-Seoud, M. S.: Numerische Behandlung von schwach singul\u00e4ren Integralgleichungen 1. Art. Dissertation, Technische Hochschule Darmstadt, D 17, 1979."},{"key":"BF02253319_CR2","series-title":"NBS","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"M. Abramowitz","year":"1965","unstructured":"Abramowitz, M., Stegun, I. A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. NBS, AMS 55. Washington, D.C.: U.S. Government Printing Office 1965."},{"key":"BF02253319_CR3","volume-title":"Treatment of Integral Equations by Numerical Methods","year":"1982","unstructured":"Baker, C. T. H., Miller, G. F. (eds.): Treatment of Integral Equations by Numerical Methods. (Proceedings of a Symposium, Durham, England, 19\u201329 July 1982.) London-New York: Academic Press 1982."},{"key":"BF02253319_CR4","volume-title":"Taschenbuch der Mathematik","author":"I. N. Bronstein","year":"1971","unstructured":"Bronstein, I. N., Semendjajew, K. A.: Taschenbuch der Mathematik, 11. Aufl. Z\u00fcrich-Frankfurt\/M: Harri Deutsch 1971.","edition":"11. Aufl."},{"key":"BF02253319_CR5","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1007\/BF01931809","volume":"11","author":"S. Christiansen","year":"1971","unstructured":"Christiansen, S.: Numerical solution of an integral equation with a logarithmic kernel. BIT11, 276\u2013287 (1971).","journal-title":"BIT"},{"key":"BF02253319_CR6","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1093\/imamat\/16.2.143","volume":"16","author":"S. Christiansen","year":"1975","unstructured":"Christiansen, S.: Integral equations without a unique solution can be made useful for solving some plane harmonic problems. J. Inst. Math. Appl.16, 143\u2013159 (1975).","journal-title":"J. Inst. Math. Appl."},{"key":"BF02253319_CR7","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1093\/imamat\/18.3.295","volume":"18","author":"S. Christiansen","year":"1976","unstructured":"Christiansen, S., Rasmussen, H.: Numerical solutions for two-dimensional annular electrochemical machining problems. J. Inst. Math. Appl.18, 295\u2013307 (1976).","journal-title":"J. Inst. Math. Appl."},{"key":"BF02253319_CR8","series-title":"International Series of Numerical Mathematics","first-page":"73","volume-title":"Numerical Treatment of Integral Equations","author":"S. Christiansen","year":"1980","unstructured":"Christiansen, S.: 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.) Albrecht, J., Collatz, L. (eds.), 73\u201391. Basel: Birkh\u00e4user 1980."},{"key":"BF02253319_CR9","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1002\/mma.1670030126","volume":"3","author":"S. Christiansen","year":"1981","unstructured":"Christiansen, S.: Condition number of matrices derived from two classes of integral equations. Math. Methods Appl. Sci.3, 364\u2013392 (1981).","journal-title":"Math. Methods Appl. Sci."},{"key":"BF02253319_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00036818208839372","volume":"13","author":"S. Christiansen","year":"1982","unstructured":"Christiansen, S.: On two methods for elimination of non-unique solutions of an integral equation with logarithmic kernel. Applicable Anal.13, 1\u201318 (1982).","journal-title":"Applicable Anal."},{"key":"BF02253319_CR11","first-page":"13","volume-title":"Treatment of Integral Equations by Numerical Methods","author":"S. Christiansen","year":"1982","unstructured":"Christiansen, S.: A comparison of various integral equations for treating the Dirichlet problem. In: [3] Baker, C. T. H., Miller, G. F. (eds.): Treatment of Integral Equations by Numerical Methods. (Proceedings of a Symposium, Durham, England, 19\u201329 July 1982). London-New York: Academic Press 1982, 13\u201324."},{"key":"BF02253319_CR12","doi-asserted-by":"crossref","first-page":"T341","DOI":"10.1002\/zamm.19830630802","volume":"63","author":"S. Christiansen","year":"1983","unstructured":"Christiansen, S.: Numerical investigation of an integral equation of Hsiao and MacCamy. Zeit. Angew. Math. Mech.63, T341-T343 (1983). (Sonderheft, GAMM-Tagung, Budapest 1982.)","journal-title":"Zeit. Angew. Math. Mech."},{"key":"BF02253319_CR13","volume-title":"Analytische Geometrie spezieller ebener Kurven","author":"K. Fladt","year":"1962","unstructured":"Fladt, K.: Analytische Geometrie spezieller ebener Kurven, Frankfurt a. M.: Akademische Verlagsgesellschaft 1962."},{"key":"BF02253319_CR14","volume-title":"A Table of Series and Products","author":"E. R. Hansen","year":"1975","unstructured":"Hansen, E. R.: A Table of Series and Products. Englewood Cliffs, N. J.: Prentice-Hall 1975."},{"key":"BF02253319_CR15","unstructured":"Hsiao, G. C.: On the stability of integral equations of the first kind with logarithmic kernel. Arch. Rat. Mech. Anal."},{"key":"BF02253319_CR16","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1137\/1015093","volume":"15","author":"G. Hsiao","year":"1973","unstructured":"Hsiao, G., MacCamy, R. C.: Solution of boundary value problems by integral equations of the first kind. SIAM Rev.15, 687\u2013705 (1973).","journal-title":"SIAM Rev."},{"key":"BF02253319_CR17","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF02259638","volume":"25","author":"G. C. Hsiao","year":"1980","unstructured":"Hsiao, G. C., Kopp, P., Wendland, W. L.: A Galerkin collocation method for some integral equations of the first kind. Computing,25, 89\u2013130 (1980).","journal-title":"Computing"},{"key":"BF02253319_CR18","doi-asserted-by":"crossref","unstructured":"Hsiao, G. C., Kopp, P., Wendland, W. L.: Some applications of a Galerkin-collocation method for boundary integral-equations of the first kind. Math. Methods Appl. Sci.6 (1984).","DOI":"10.1002\/mma.1670060119"},{"key":"BF02253319_CR19","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/0022-247X(77)90186-X","volume":"58","author":"G. C. Hsiao","year":"1977","unstructured":"Hsiao, G. C., Wendland, W. L.: A finite element method for some integral-equations of the first kind. J. Math. Anal. Appl.58, 449\u2013481 (1977).","journal-title":"J. Math. Anal. Appl."},{"key":"BF02253319_CR20","unstructured":"IMSL (International Mathematical & Statistical Libraries, Inc., 7500 Bellaire Blvd., Houston, Texas, U.S.A.). LSVDF (singular value decomposition of a real matrix). IMSL Library, Ed. 8, June 1981."},{"key":"BF02253319_CR21","volume-title":"Die Grundlehren der mathematischen Wissenschaften, Band 180","author":"N. S. Landkof","year":"1972","unstructured":"Landkof, N. S.: Foundations of Modern Potential Theory. (Die Grundlehren der mathematischen Wissenschaften, Band 180.) Berlin-Heidelberg-New York: Springer 1972."},{"key":"BF02253319_CR22","volume-title":"Some Basic Problems of the Mathematical Theory of Elasicity","author":"N. I. Muskhelishvili","year":"1963","unstructured":"Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasicity, Second English Edition. Groningen: Noordhoff 1963.","edition":"Second English"},{"key":"BF02253319_CR23","volume-title":"Stress Concentration Around Holes","author":"G. N. Savin","year":"1961","unstructured":"Savin, G. N.: Stress Concentration Around Holes. New York-Oxford-London-Paris: Pergamon Press 1961."},{"key":"BF02253319_CR24","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/BF02162876","volume":"10","author":"G. T. Symm","year":"1967","unstructured":"Symm, G. T.: Numerical mapping of exterior domains. Numer. Math.10, 437\u2013445 (1967).","journal-title":"Numer. Math."},{"key":"BF02253319_CR25","first-page":"463","volume-title":"Treatment of Integral Equations by Numerical Methods","author":"W. L. Wendland","year":"1982","unstructured":"Wendland, W. L.: On applications and the convergence of boundary integral methods. In: [3] Baker, C. T. H., Miller, G. F. (eds.): Treatment of Integral Equations by Numerical Methods. (Proceedings of a Symposium, Durham, England, 19\u201329 July 1982.) London-New York: Academic Press 1982, 463\u2013476."},{"key":"BF02253319_CR26","unstructured":"Wendland, W. L., Christiansen, S.: On the condition number of the influence matrix belonging to some first kind integral equations with logarithmic kernel. Applicable Anal."},{"key":"BF02253319_CR27","volume-title":"A Survey of Numerical Mathematics, I+II","author":"D. M. Young","year":"1973","unstructured":"Young, D. M., Gregory, R. D.: A Survey of Numerical Mathematics, I+II. Reading, Mass: Addison-Wesley 1973."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02253319.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02253319\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02253319","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T14:52:23Z","timestamp":1558018343000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02253319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,9]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1985,9]]}},"alternative-id":["BF02253319"],"URL":"https:\/\/doi.org\/10.1007\/bf02253319","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,9]]}}}