Smooke, M. D. Error estimate for the modified Newton method with applications to the solution of nonlinear, two-point boundary-value problems. (English) Zbl 0487.65045 J. Optimization Theory Appl. 39, 489-511 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 17 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:nonlinear, two-point boundary value problems; factorization of a Jacobian matrix; modified Newton method; error estimate; combustion PDFBibTeX XMLCite \textit{M. D. Smooke}, J. Optim. Theory Appl. 39, 489--511 (1983; Zbl 0487.65045) Full Text: DOI References: [1] Kantorovich, L. V., andAkilov, G. P.,Functional Analysis in Normed Spaces, Pergamon Press, Oxford, England, 1964. · Zbl 0127.06104 [2] Smooke, M. D.,Solution of Burner-Stabilized Premixed Laminar Flames by Boundary-Value Methods, Journal of Computational Physics (to appear). · Zbl 0492.65065 [3] Henrici, P.,Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York, New York, 1962. · Zbl 0112.34901 [4] Isaacson, E., andKeller, H. B.,Analysis of Numerical Methods, John Wiley and Sons, New York, New York, 1966. · Zbl 0168.13101 [5] Roberts, S. M., andShipman, J. S.,Two-Point Boundary-Value Methods: Shooting Methods, Elsevier, New York, New York, 1972. · Zbl 0239.65061 [6] Ascher, U., Christiansen, J., andRussell, R. D.,COLSYS: A Collocation Code for Boundary-Value Problems, Codes for Boundary Value Problems in ODE’s, Edited by B. Childs et al., Springer Verlag, New York, New York, 1979. · Zbl 0459.65061 [7] Keller, H. B.,Accurate Difference Methods for Nonlinear, Two-Point Boundary-Value Problems, SIAM Journal on Numerical Analysis, Vol. 11, No. 2, 1974. · Zbl 0282.65065 [8] Eberius, K. H., Hoyermann, K., andWagner, H. G.,Experimental and Mathematical Study of a Hydrogen-Oxygen Flame, 13th International Symposium on Combustion, Combustion Institute, Pittsburg, Pennsylvania, 1971. [9] Peeters, J., andMahnen, G.,Reaction Mechanisms and Rate Constants of Elementary Steps in Methane-Oxygen Flames, 14th International Symposium on Combustion, Combustion Institute, Pittsburg, Pennsylvania, 1973. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.