Stability of Nonlinear Computing Schemes

Previous article Next article Stability of Nonlinear Computing SchemesT. S. TuckerT. S. Tuckerhttps://doi.org/10.1137/0706007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Hans H. Ehrmann, On implicit function theorems and the existence of solutions of non-linear equations, Enseignement Math. (2), 9 (1963), 129–176 MR0156175 0127.08004 Google Scholar[2] L. V. Kantorovich and , G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964xiii+771 MR0213845 0127.06104 Google Scholar[3] Milton Lees, J. Bramble, Discrete methods for nonlinear two-point boundary value problemsNumerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, New York, 1966, 59–72 MR0202323 0148.39206 Google Scholar[4] S. G. Mihlin, Some stability conditions for the Ritz problem, Vestnik Leningrad. Univ., 16 (1961), 40–51 MR0139263 Google Scholar[5] S. G. Mihlin, On the stability of certain computational processes, Dokl. Akad. Nauk SSSR, 157 (1964), 271–273, Soviet Math. Dokl., 5 (1964), pp. 931–933. MR0182138 0131.13801 Google Scholar[6] W. V. Petryshyn, Iterative construction of fixed points of contractive type mappings in Banach spacesNumerical Analysis of Partial Differential Equations (C.I.M.E. 2 Ciclo, Ispra, 1967), Edizioni Cremonese, Rome, 1968, 307–339, Lecture notes MR0250435 0187.09301 Google Scholar[7] W. V. Petryshyn, On nonlinear P-compact operators in Banach space with applications to constructive fixed-point theorems, J. Math. Anal. Appl., 15 (1966), 228–242 10.1016/0022-247X(66)90114-4 MR0202014 0149.10602 CrossrefISIGoogle Scholar[8] W. V. Petryshyn, Projection methods in nonlinear numerical functional analysis, J. Math. Mech., 17 (1967), 353–372 MR0218941 0162.20202 ISIGoogle Scholar[9] P. A. Raviart, Methode de Newton dans les equations aux derivées partielles nonlinéaires, Lecture notes, Centro Internazionale Matematico Estivo, Ispra, 1967 Google Scholar[10] A. T. Taldykin, Systems of elements of a Hilbert space and series formed from them, Mat. Sbornik N.S., 29(71) (1951), 79–120 MR0043382 Google Scholar[11] G. Vainikko, On the convergence of the collocation method for nonlinear differential equations, Z. Vyčisl. Mat. i Mat. Fiz., 6 (1966), 35–42 MR0196945 0154.17301 Google Scholar[12] G. N. Jaskova and , M. N. Jakovlev, Some conditions for stability of the Petrov-Galerkin method, Trudy Mat. Inst. Steklov., 66 (1962), 182–189 MR0155207 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Note on the Galerkin Method's StabilityMathematische Nachrichten, Vol. 176, No. 1 Cross Ref Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. IIMark J. Friedman17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 18, No. 4AbstractPDF (797 KB)Stability of the Rayleigh-Ritz procedure for nonlinear two-point boundary value problemsNumerische Mathematik, Vol. 24, No. 1 Cross Ref On the stability of the Ritz-Galerkin method for Hammerstein equations1 January 1975 | Mathematics of Computation, Vol. 29, No. 130 Cross Ref On the stability of the Ritz procedure for nonlinear problemsNumerische Mathematik, Vol. 23, No. 4 Cross Ref Zur Struktur eines Algorithmus zur Lösung freier Randwertprobleme parabolischer Differentialoperatoren23 August 2006 Cross Ref Stability of Ritz procedure for nonlinear two-point boundary value problemNumerische Mathematik, Vol. 20, No. 3 Cross Ref A General Theory of Convergence for Numerical MethodsBruce Chartres and Robert Stepleman14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 3AbstractPDF (1392 KB) Volume 6, Issue 1| 1969SIAM Journal on Numerical Analysis History Submitted:14 November 1967Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706007Article page range:pp. 72-81ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics