Publication Cover
Applicable Analysis
An International Journal
Volume 8, 1978 - Issue 1
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Original Articles

On singular singularly-perturbed initial value problems

Pages 71-81 | Published online: 04 Mar 2011

References

  • Butuzov , V. F. and Vasil'eva , A. B. 1970 . Differential and difference equation systems with a . Soviet Math. Dokl. , 6 : 499 – 510 .
  • Cesari , L. 1975 . “ Alternative methods in nonlinear analysis,” . In International Conference on Differential Equations , Edited by: Antosiewicz , H. A. 95 – 148 . New York : Academic Press .
  • Fife , P. C. 1972 . Singular perturbation problems whose degenerate forms have many solutions . Applicable Analysis , 1 : 331 – 358 .
  • Golub , G. H. 1965 . Numerical methods for solving linear least squares problems . Numer Math. , 7 : 206 – 216 .
  • Golub , G. H. and Pereyra , V. 1976 . “ Differentiation of pseudoinverses, separable nonlinear least square problems, and other tales” . In Generalized Inverses and Applications , Edited by: Nashed , M. Z. 303 – 324 . New York : Academic Press .
  • Gordon , N. 1975 . Matched asymptotic expansion solutions of nonlinear partial differential equations with a small parameter” . SIAM J. Math. Anal. , 6 : 1007 – 1016 .
  • Hoppensteadt , F.C. 1966 . Singular perturbations on the infinite interval . Trans. Amer. Math. Soc. , 123 : 521 – 535 .
  • Hoppensteadt , F. 1971 . Properties of solutions of ordinary differential equations with a small parameter . Comm. Pure Appl. Math. , 24 : 807 – 840 .
  • Hoppensteadt , F. C. and Miranker , W. L. 1976 . ”Differential equations having rapidly . J. Differential Equations , 22 : 237 – 249 .
  • Kersten , P. H. M. March 1972 . “ Uniform asymptotic expansions for a class of nonlinear systems of differential equations containing a small parameter ” . March , Twente University of Technology . report
  • Levin , J. J. 1957 . The asymptotic behavior of the stable initial manifolds of a system of nonlinear differential equations . Trans. Amer. Math. Soc. , 85 March : 357 – 368 .
  • O'Malley , R. E. Jr. 1974 . Introduction to Singular Perturbations , New York : Academic Press .
  • O'Malley , R. E. Jr. 1977 . High gain feedback systems as singular singular-perturbation problems” . Joint Automatic Control Conference . 1977 . pp. 1278 – 1281 .
  • O'Malley , R. E. Jr. “ Partially singular control problems as singular singular-perturbation problems” . 957 – 961 . Seventh IFAC Congress .
  • Flaherty , J. E. 1977 . “ Singular singular-perturbation problems” . In Lecture Notes in Math. , Vol. 594 , 422 – 436 . Berlin : Springer-Verlag .
  • Stewart , G. W. 1973 . Introduction to Matrix Computations , New York : Academic Press .
  • Tihonov , A. N. 1952 . Systems of differential equations containing small parameters in the derivatives . Mat. Sb. , 31 ( 73 ) : 575 – 586 .
  • Turrittin , H. L. 1952 . Asymptotic expansions of solutions of systems of ordinary differential equations containing a parameter . Contrib. Theory Nonlinear Oscillations , 2 ( 73 ) : 81 – 116 .
  • Tihonov , A. N. 1975 . Soviet Math. Dokl. , 16 ( 73 ) : 1121 – 1125 .
  • Wasow , W. 1965 . Asymptotic Expansions for Ordinary Differential Equations , New York : Wiley .

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