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Singularly perturbed systems of Volterra equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Singularly perturbed linear Volterra integral equations are solved in this paper. To improve the results which has been published earlier, formal solutions of systems of equations are determined and rigorously proved to be asymptotic to the exact solutions.
Wydawca
Rocznik
Strony
221--244
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • Temporary at: Department of Mathematics and Applied Mathematics university of cape Town, RSA ; Department of Mathematics University of Dar Es Salaam P.O. Box 35062, Dar Es Salaam Tanzania, abijura@maths.uct.ac.za
Bibliografia
  • [1] Angell, J. S., Olmstead, W. E., Sinqularly perturbed Volterra inteqral equations, SIAM J. Appl. Math. 47(1) (1987), 1-14.
  • [2] Angell, J. S., Olmstead, W. E., Singularly perturbed Volterra integral equations, SIAM J. Appl. Math. 47(6) (1987), 1150-1162.
  • [3] Angell, J. S., Olmstead, W. E., Singularly perturbed integral equations with end point boundary layers, SIAM J. Appl. Math. 49 (1989), 1567-1584.
  • [4] Flatto, L., Levinson, N., Periodic solutions of singularly perturbed systems, J. Rational Mech. Anal. 4 (1955), 943-950.
  • [5] Gripenberg, G. Londen, S-O., StafFans, O., Volterra Integral and Functional Equations, in “Encyclopedia of Mathematics and Its Application”, Cambridge University Press, Cambridge, New York, 1990.
  • [6] Hirsch, W. M., Smale, S., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York, 1974.
  • [7] Hoppensteadt, F. C., Singular perturbations on the infinite interval, Trans. Amer. Math. Soc. 123 (1966), 521-535.
  • [8] Lange, C. G., On spurious solutions of singular perturbation problems, Stud, in Appl. Math. 68 (1983), 227-257.
  • [9] Lange, C. G., Smith, D.R., Singular perturbation analysis of integral equations, Stud. Appl. Math. 79 (1988), 1-63.
  • [10] Lange, C. G., Smith, D.R., Singular perturbation analysis of integral equations, Stud. Appl. Math. 90 (1993), 1-74.
  • [11] Miller, R. K., Nonlinear Volterra Integral Equations, W. A. Benjamin, California, 1971.
  • [12] O’Malley, R. E., Introduction to Singular Perturbation, Academic Press, New York, London, 1974.
  • [13] O’Malley, R. E., Singular Perturbation Methods for Ordinary Differential Equations, Springer-Verlag, New York, 1991.
  • [14] Skinner, L. A., Asymptotic solution to a class of singularly perturbed Volterra integral equations, Methods Appl. Anal. 2 (1995), 212-222.
  • [15] Smith, D. R., Singular Perturbation theory; An Introduction with Applications, Cambridge University Press, Cambridge, New York, 1985.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0014-0012
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