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On the numerical solution of implicit two-point boundary-value problems

Jaroslav Doležal; Jiří Fidler

Kybernetika (1979)

  • Volume: 15, Issue: 3, page (222)-230
  • ISSN: 0023-5954

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Doležal, Jaroslav, and Fidler, Jiří. "On the numerical solution of implicit two-point boundary-value problems." Kybernetika 15.3 (1979): (222)-230. <http://eudml.org/doc/28916>.

@article{Doležal1979,
author = {Doležal, Jaroslav, Fidler, Jiří},
journal = {Kybernetika},
keywords = {Numerical Solution; Quasilinearization Method; Nonlinear Implicite Two- Point Boundary-Value Problems; Comparison with the Classical Newton- Raphson Method; Ordinary Differential Equations},
language = {eng},
number = {3},
pages = {(222)-230},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the numerical solution of implicit two-point boundary-value problems},
url = {http://eudml.org/doc/28916},
volume = {15},
year = {1979},
}

TY - JOUR
AU - Doležal, Jaroslav
AU - Fidler, Jiří
TI - On the numerical solution of implicit two-point boundary-value problems
JO - Kybernetika
PY - 1979
PB - Institute of Information Theory and Automation AS CR
VL - 15
IS - 3
SP - (222)
EP - 230
LA - eng
KW - Numerical Solution; Quasilinearization Method; Nonlinear Implicite Two- Point Boundary-Value Problems; Comparison with the Classical Newton- Raphson Method; Ordinary Differential Equations
UR - http://eudml.org/doc/28916
ER -

References

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  1. A. Miele R. R. Iyer, General technique for solving nonlinear, two-point boundary-value problems via the method of particular solutions, J. Optimization Theory Appl. 5 (1970), 5, 382-399. (1970) MR0266441
  2. A. Miele R. R. Iyer, Modified quasilinearization method for solving nonlinear, two-point boundary-value problems, J. Math. Anal. Appl. 36 (1971), 3, 674-692. (1971) MR0288966
  3. A. Miele S. Naqui A. V. Levy R. R. Iyer, Numerical solution of nonlinear equations and nonlinear, two-point boundary-value problems, In "Advances in Control Systems: Theory and Applications", Vol. 8, C. T. Leondes (ed.), Academic Press, New York 1971, 189-215. (1971) 
  4. S. M. Roberts J. S. Shipman, On the Miele-Iyer modified quasilinearization method, J. Optimization Theory Appl. 14 (1974), 4, 381-391. (1974) MR0356522
  5. J. Fidler, The application of the modified quasilinearization method for the solution of continuous time boundary-value problems, Research Report No. 819. Institute of Information Theory and Automation, Prague 1977. In Czech. (1977) 
  6. J. Doležal, On the modified quasilinearization method for discrete two-point boundary-value problems, Research Report No. 788, Institute of Information Theory and Automation, Prague 1977. (1977) 
  7. J. Doležal, On a certain type of discrete two-point boundary-value problems arising in discrete optimal control, EQUADIFF 4 Conference, Prague, August 22-26, 1977. See also: Kybernetika 15 (1979), 3, 215-221. (1977) MR0542177
  8. J. Doležal J. Fidler, To the problem of numerical solution of implicit two-point boundary-value problems, Research Report No. 857, Institute of Information Theory and Automation, Prague 1978. In Czech. (1978) 
  9. J. Doležal, Modified quasilinearization method for the solution of implicit, nonlinear, two-point boundary-value problems for systems of difference equations, The 5th Symposium on Algorithms ALGORITMY' 79, High Tatras, April 23-27, 1979. In Czech. (1979) 
  10. M. R. Hestenes, Calculus of Variations and Optimal Control Theory, Wiley, New York 1966. (1966) Zbl0173.35703MR0203540
  11. D. G. B. Edelen, Differential procedures for systems of implicit relations and implicitly coupled nonlinear boundary-value problems, In "Numerical Methods for Differential Systems: Recent Development in Algorithm, Software, and Applications", L. Lapidus, W. E. Schiesser (eds.), Academic Press, New York 1976, 85-95. See also: In "Mathematical Models and Numerical Methods", Banach Center Publications Vol. 3, A. N. Tichonov et al. (eds.), PWN-Polish Scientific Publishers, Warszawa 1978, 289-296. (1976) MR0458856
  12. S. M. Roberts J. S. Shipman, Two-Point Boundary Value Problems: Shooting Methods, American Elsevier, New York 1972. (1972) MR0323119
  13. E. Polak, Computational Methods in Optimization: Unified Approach, Academic Press, New York 1971. (1971) MR0282511

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