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Previous article Next article The Numerical Solution of Some Biharmonic Problems by Mathematical Programming TechniquesJ. R. Cannon and Maria M. CecchiJ. R. Cannon and Maria M. Cecchihttps://doi.org/10.1137/0703039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Heinrich Behnke and , Friedrich Sommer, Theorie der analytischen Funktionen einer komplexen Veränderlichen., Zweite veränderte Auflage. Die Grundlehren der mathematischen Wissenschaften, Bd. 77, Springer-Verlag, Berlin, 1962, 128– MR0147622 0101.29502 CrossrefGoogle Scholar[2] J. R. Cannon, The numerical solution of the Dirichlet problem for Laplace's equation by linear programming, J. Soc. Indust. Appl. Math., 12 (1964), 233–237 10.1137/0112022 MR0164453 0221.65186 LinkISIGoogle Scholar[3] J. R. Cannon and , Keith Miller, Some problems in numerical analytic continuation, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 87–98 MR0179908 0214.14805 LinkGoogle Scholar[4] T. Carleman, Fonctions Quasi Analytiques, Gauthier-Villars, Paris, 1926, 3–5 Google Scholar[5] Jim Douglas, Jr., R. E. Langer, A numerical method for analytic continuation, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, 1960, 179–189 MR0117866 0100.12405 Google Scholar[6] Saul I. Gass, Linear programming: methods and applications, McGraw-Hill Book Co., Inc., New York, 1958xii+223 MR0096554 0081.36702 Google Scholar[7] Fritz John, Continuous dependence on data for solutions of partial differential equations with a presribed bound, Comm. Pure Appl. Math., 13 (1960), 551–585 MR0130456 0097.08101 CrossrefISIGoogle Scholar[8] G. Lauricella, Integrazione dell' equazione $\Delta^{2}(\Delta^{2}u)=0$ in un campo di forma circolare, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 31 (1895–1896), 610–618 Google Scholar[9] O. L. Mangasarian, Numerical solution of the first biharmonic problem by linear programming, Internat. J. Engrg. Sci., 1 (1963), 231–240 10.1016/0020-7225(63)90035-1 MR0149684 0137.13904 CrossrefGoogle Scholar[10] K. Miller, Least squares methods for improperly posed problems with a prescribed bound, to appear Google Scholar[11] Carlo Miranda, Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche de due variabili, Giorn. Mat. Battaglini (4), 2(78) (1948), 97–118 MR0030058 0037.07103 Google Scholar[12] M. Picone, Nuovi indirizzi di ricerca nella teoria e nel calcolo delle soluzioni di talune equazioni lineari alle derivate parziali della f sica matematica, Ann. Scuola Norm. Sup. Pisa, 5 (1936), 213–288 0014.26102 Google Scholar[13] Åke Pleijel, On Green's functions for elastic plates with clamped, supported and free edges, Proceedings of the Symposium on Spectral Theory and Differential Problems, Oklahoma Agricultural and Mechanical College, Stillwater, Okla., 1951, 413–437 MR0047891 0068.08502 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Iterative Method to Solve a Data Completion Problem for Biharmonic Equation for Rectangular Domain2 September 2017 | Annals of West University of Timisoara - Mathematics and Computer Science, Vol. 55, No. 1 Cross Ref The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equationMathematical and Computer Modelling, Vol. 42, No. 3-4 Cross Ref A numerical method for an inverse biharmonic problemInverse Problems in Engineering, Vol. 7, No. 5 Cross Ref A comparison of different methods to solve inverse biharmonic boundary value problemsInternational Journal for Numerical Methods in Engineering, Vol. 45, No. 12 Cross Ref The boundary element solution of the Laplace and biharmonic equations subjected to noisy boundary dataInternational Journal for Numerical Methods in Engineering, Vol. 43, No. 3 Cross Ref A alternating boundary element method for solving cauchy problems for the biharmonic equationInverse Problems in Engineering, Vol. 5, No. 2 Cross Ref Mathematical programming techniques to solve biharmonic problems by a recursive projection algorithmJournal of Computational and Applied Mathematics, Vol. 32, No. 1-2 Cross Ref Improved Stability Estimates for Classes of Illposed Cauchy Problems2 May 2007 | Applicable Analysis, Vol. 19, No. 2-3 Cross Ref Recent Developments in the Numerical Solution of Partial Differential Equations by Linear ProgrammingTo-Yat Cheung10 July 2006 | SIAM Review, Vol. 20, No. 1AbstractPDF (2684 KB)A review of least-squares methods for solving partial differential equationsInternational Journal for Numerical Methods in Engineering, Vol. 10, No. 5 Cross Ref The numerical solution of some elliptic boundary value problems by integral operator methods26 August 2006 Cross Ref Constructive Approximation of Solutions to Linear Elliptic Boundary Value ProblemsN. L. Schryer14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 4AbstractPDF (2179 KB)Determination of an unknown forcing function in a hyperbolic equation from overspecified dataAnnali di Matematica Pura ed Applicata, Vol. 85, No. 1 Cross Ref Applications of Linear Programming to Numerical AnalysisPhilip Rabinowitz18 July 2006 | SIAM Review, Vol. 10, No. 2AbstractPDF (3637 KB)Numerical Experiments on the Solution of Some Biharmonic Problems by Mathematical Programming TechniquesJ. R. Cannon and Maria M. Cecchi14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 4, No. 2AbstractPDF (575 KB) Volume 3, Issue 3| 1966SIAM Journal on Numerical Analysis History Submitted:01 December 1965Published online:14 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0703039Article page range:pp. 451-466ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics

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