SC-90-09.pdf - ZIB

More documents

Recommendations

Info

References [1] E. L. Allgower, K. Böhmer: Application of the mesh independence principle to mesh refinement strategies. SIAM J. Numer. Anal. 24, pp. 1335-1351 (1987). [2] E. L. Allgower, K. Böhmer, F. A. Potra, W. C. Rheinboldt: A meshindependence principle for operator equations and their discretizations. SIAM J. Numer. Anal., 23, pp. 160-169 (1986). [3] U. M. Ascher, R.M.M. Mattheij, R. D. Russell: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Prentice Hall Series in Computational Mathematics (1988\ [4] G. Bader: Numerische Behandlung von Randwertproblemen für Funktionaldifferentialgleichungen. Universität Heidelberg, Inst. Angew. Math.: Dissertation (1983). [5] H. G. Bock: Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics. In Ebert, K. H., Deuflhard, P., Jäger, W. (eds.): Modelling of Chemical Reaction Systems. Berlin-Heidelberg-New York: Springer Ser. Chem. Phys., vol. 18, pp. 102-125 (1981). [6] C. de Boor, B. Swartz: Collocation at Gaussian Points. SIAM J. Numer. Anal. 10, pp. 582-606 (1973). [7] P. Deuflhard, G. Heindl: Affine invariant convergence theorems for Newton's method and extensions to related methods. SIAM J. Numer. Anal. 16, pp. 1-10 (1979). [8] L. Kantorovitch: On Newton's Method for Functional Equations. (Russian), Dokl. Akad. Nauk SSSR 59, pp. 1237-1249 (1948). [9] S. F. McCormick: A revised mesh refinement strategy for Newton's method applied to nonlinear two-point boundary value problems. Lecture Notes in Mathematics 679, Springer-Verlag Berlin, pp. 15-23 (1978). [10] I. Mysovskii: On convergence of Newton's method. (Russian), Trudy Mat. Inst. Steklov 28, pp. 145-147 (1949). [11] F. A. Potra, V. Ptäk: Nondiscrete Induction and Iterative Processes. Pittman, London (1984). 19
[12] L. B. Rail: A Note on the Convergence of Newton's Method. SIAM J. Numer. Anal. 11, pp. 34-36 (1974). [13] T. Yamamoto: A Unified Derivation of Several Error Bounds for Newton's Process. J. Comp. Appl. Math 12/13, pp. 179-191 (1985). 20
Page 1 and 2: Konrad-Zuse-Zentrum für Informatio
Page 3 and 4: The authors wish to thank Erlinda C
Page 5 and 6: 1. A Refined Newton-Mysovskii Theor
Page 7 and 8: We note that under the hypothesis o
Page 9 and 10: Indeed (1.6) follows from (1.21) by
Page 11 and 12: 2. Asymptotic Mesh Independence of
Page 13 and 14: C\: if Wj G Xj and w € X are solu
Page 15 and 16: and by using property C 0 we obtain
Page 17 and 18: then for k > k(x°,e), where \x —
Page 19 and 20: Condition (2.30) is generally not s
Page 21: implies (2.12) — without any quas

SC-90-09.pdf - ZIB

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?