On Urabe's application of Newton's method to nonlinear boundary value problems

Ravi P. Agarwal

Archivum Mathematicum (1984)

  • Volume: 020, Issue: 3, page 113-123
  • ISSN: 0044-8753

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Agarwal, Ravi P.. "On Urabe's application of Newton's method to nonlinear boundary value problems." Archivum Mathematicum 020.3 (1984): 113-123. <http://eudml.org/doc/18136>.

@article{Agarwal1984,
author = {Agarwal, Ravi P.},
journal = {Archivum Mathematicum},
keywords = {contraction mapping principle; approximate solution},
language = {eng},
number = {3},
pages = {113-123},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Urabe's application of Newton's method to nonlinear boundary value problems},
url = {http://eudml.org/doc/18136},
volume = {020},
year = {1984},
}

TY - JOUR
AU - Agarwal, Ravi P.
TI - On Urabe's application of Newton's method to nonlinear boundary value problems
JO - Archivum Mathematicum
PY - 1984
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 020
IS - 3
SP - 113
EP - 123
LA - eng
KW - contraction mapping principle; approximate solution
UR - http://eudml.org/doc/18136
ER -

References

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  2. R. P. Agarwal, Component-wise convergence in quasilinearization, Proc. Indian Acad. Sci. Sec. A. 86 (1977), 519-529. (1977) MR0492473
  3. R. P. Agarwal, On periodic solutions of nonlinear second order differential systems, J. Comp. Appl. Math. 5 (1979), 117-123. (1979) Zbl0407.34021MR0536248
  4. R. P. Agarwal, Jaromír Vosmanský, Two-point boundary value problems for second order systems, Arch. Math. (Brno), 19 (1983), 1-8. (1983) MR0724304
  5. R. P. Agarwal, Contraction and approximate contraction with an application to multi-point boundary value problems, J. Comp. Appl. Math. 9 (1983), 315-325. (1983) Zbl0546.65060MR0729235
  6. G. Anichini, Nonlinear problems for systems of differential equations, Nonlinear Analysis. Theory, Methods and Applications, 1 (1977), 691-699. (1977) Zbl0388.34011MR0592963
  7. S. R. Bernfeld, V. Lakshmikantham, An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York, 1974. (1974) Zbl0286.34018MR0445048
  8. L. Collatz, Functional Analysis and Numerical Mathematics, Academic Press, New York, 1974. (1974) MR0205126
  9. R. Conti, Recent trends in the theory of boundary value problems for ordinary differential equations, Boll. UMI, 22 (1967), 135-178. (1967) Zbl0154.09101MR0218650
  10. P. L. Falb, J. L. de Jong, Some Successive Approximation Methods in Control and Oscillation Theory, Academic Press, New York, 1969. (1969) Zbl0202.09603MR0264855
  11. A. Perov, A. Kibenko, On a certain general method for investigation of boundary value problems, Izv. Akad. Nauk SSSR 30 (1966), 249-264. (1966) MR0196534
  12. J. Schröder, Das Iterationsverfahren bei verallgemeinertem Abstandsbegriff, Math. Z. 60 (1956), 111-116. (1956) MR0083816
  13. M. Urabe, An existence theorem for multi-point boundary value problems, Funkcialaj Ekvacioj, 9 (1966), 43-60. (1966) Zbl0168.06502MR0209558
  14. M. Urabe, The Newton method and its applications, Proc. US-Japan seminar on differential and functional equations, (1967), 383-410. (1967) MR0223628
  15. M. Urabe, Component-wise error analysis of iterative methods practiced on a floating-point system, Mem. Fac. Sci. Kyushu Univ. Ser. A. 27 (1973), 23-64. (1973) Zbl0277.65034MR0323099
  16. M. Urabe, A posteriori component-wise error estimation of approximate solutions to nonlinear equations, Lecture notes in Computer science 29, Interval Mathematics, Springer-Verlag (1975), 99-117. (1975) Zbl0306.65031
  17. M. Urabe, On the Newton method to solve problems of the least squares type for ordinary differential equations, Proc. Int. Symp. Dynamical Systems, Providence, (1974), 1-7. (1974) MR0375791
  18. M. Urabe, On the Newton method to solve problems of the least squares type for ordinary differential equations, Mem. Fac. Sci. Kyushu Univ., Ser. A, 29 (1975), 173-183. (1975) Zbl0357.65055MR0375791

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