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Slow/fast decoupling for linear boundary value problems

  • Part 2 Survey Papers With Research Aspects
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Asymptotic Analysis II —

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 985))

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References

  1. R. C. Aiken, editor, Proceedings, International Conference on Stiff Computation, Park City, 1982.

    Google Scholar 

  2. L. R. Anderson, Decoupling and Reduced Order Modeling of Two-Time-Scale Control Systems, doctoral dissertation, University of Arizona, Tucson, 1979.

    Google Scholar 

  3. U. Ascher and R. Weiss, "Collocation for singular perturbation problems II: Linear first order systems without turning points," Technical Report 82-4, Department of Computer Science, University of British Columbia, Vancouver, 1982.

    MATH  Google Scholar 

  4. A. Bjorck, "A block QR algorithm for the partitioning of stiff differential systems," abstract, SIAM 30th Anniversary Meeting, Stanford, 1982.

    Google Scholar 

  5. D. L. Brown, Solution Adaptive Mesh Procedures for the Numerical Solution of Singular Perturbation Problems, thesis, California Institute of Technology, Pasadena, 1982.

    Google Scholar 

  6. J. H. Chow, B. Avramovic, P. V. Kokotovic, and J. R. Winkelman, "Singular perturbations, coherency and aggregation of dynamic systems," Report, Electric Utility Systems Engineering Department, General Electric Company, Schenectady, 1981.

    MATH  Google Scholar 

  7. W. E. Ferguson, Jr., A Singularly Perturbed Linear Two-Point Boundary Value Problem, thesis, California Institute of Technology, Pasadena, 1975.

    Google Scholar 

  8. J. E. Flaherty and W. Mathon, "Collocation with polynomial and tension splines for singularly perturbed boundary value problems," SIAM J. Sci. Stat. Comput. 1 (1980), 260–289.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. E. Flaherty and R. E. O’Malley, Jr., "Asymptotic and numerical methods for vector systems of singularly perturbed boundary value problems," Proceedings, Army Numerical Analysis and Computer Conference, Vicksburg, 1982.

    Google Scholar 

  10. H. Gingold and P.-F. Hsieh, "On global simplification of a singularly perturbed system of linear ordinary differential equations," preprint, West Virginia and Western Michigan Universities, 1982.

    Google Scholar 

  11. G. H. Golub and J. H. Wilkinson, "Ill-conditioned eigen-systems and the computation of the Jordan canonical form," SIAM Review 18 (1976), 578–619.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. A. Harris, Jr., "Singularly perturbed boundary value problems revisited," Lecture Notes in Math. 312, Springer-Verlag, Berlin, 1973, 54–64.

    MATH  Google Scholar 

  13. D. L. Hetrick et al., "Solution methods for simulation of nuclear power systems," Report NP-1928, Electric Power Research Institute, Palo Alto, 1981.

    Google Scholar 

  14. F. C. Hoppensteadt and W. L. Miranker, "Differential equations having rapidly changing solutions: Analytic methods for weakly nonlinear systems," J. Differential Equations 22 (1976), 237–249.

    Article  MathSciNet  MATH  Google Scholar 

  15. V. C. Klema and A. J. Laub, "The singular value decomposition: Its computation and some applications," IEEE Trans. Automatic Control 25 (1980), 164–176.

    Article  MathSciNet  MATH  Google Scholar 

  16. B. Kreiss and H.-O. Kreiss, "Numerical methods for singular perturbation problems," SIAM J. Numer. Anal. 18 (1981), 262–276.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Leveque and J. Oliger, "Numerical methods based on additive splittings for hyperbolic partial differential equations," Report No. 81-16, Computer Science Department, Stanford University, 1981.

    Google Scholar 

  18. R. M. M. Mattheij, "Riccati-type transformations and decoupling of singularly perturbed ODE," Proceedings, International Conference on Stiff Computation, Park City, 1982.

    Google Scholar 

  19. R. M. M. Mattheij and R. E. O’Malley, Jr., "Decoupling of boundary value problems for two-time-scale systems," Proceedings, International Conference on Stiff Computation, Park City, 1982.

    Google Scholar 

  20. R. M. M. Mattheij and G. W. M. Staarink, "An efficient algorithm for solving general linear two point BVP," preprint, Rensselaer Polytechnic Institute and Katholieke Universiteit, Nijmegen, 1982.

    MATH  Google Scholar 

  21. R. E. O’Malley, Jr., "On the asymptotic solution of boundary value problems for nonhomogeneous ordinary differential equations containing a parameter," J. Math. Anal. Appl. 28 (1969), 450–460.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. E. O’Malley, Jr., "Boundary value problems for linear systems of ordinary differential equations involving many small parameters," J. Math. Mech. 18 (1969), 835–856.

    MathSciNet  MATH  Google Scholar 

  23. R. E. O’Malley, Jr., Introduction to Singular Perturbations, Academic Press, New York, 1974.

    MATH  Google Scholar 

  24. R. E. O’Malley, Jr., "Singular perturbations and optimal control," Lecture Notes in Math. 680, Springer-Verlag, Berlin, 1978, 170–218.

    MATH  Google Scholar 

  25. R. E. O’Malley, Jr., "On multiple solutions of singularly perturbed systems in the conditionally stable case," Singular Perturbations and Asymptotics, R. E. Meyer and S. V. Parter, editors, Academic Press, New York, 1980, 87–108.

    Chapter  Google Scholar 

  26. R. E. O’Malley, Jr., "Slow/fast decoupling — Analytical and numerical aspects," Proceedings, Seminar on Singular Perturbations in Systems and Control, Udine, 1982.

    Google Scholar 

  27. R. E. O’Malley, Jr. and L. R. Anderson, "Time-scale decoupling and order reduction for linear time-varying systems," Optimal Control Appl. and Methods 3 (1982), 133–153.

    Article  MathSciNet  MATH  Google Scholar 

  28. R. E. O’Malley, Jr. and J. E. Flaherty, "Analytical and numerical methods for nonlinear singular singularly-perturbed initial value problems," SIAM J. Appl. Math. 38 (1980), 225–248.

    Article  MathSciNet  MATH  Google Scholar 

  29. B. Porter and R. Crossley, Modal Control, Taylor and Francis, London, 1972.

    MATH  Google Scholar 

  30. R. J. Sacker and G. R. Sell, "Singular perturbations and conditional stability," J. Math. Anal. Appl. 76 (1980), 406–431.

    Article  MathSciNet  MATH  Google Scholar 

  31. R. E. Scheid, Jr., The Accurate Numerical Solution of Highly Oscillatory Ordinary Differential Equations, thesis, California Institute of Technology, Pasadena, 1982.

    MATH  Google Scholar 

  32. G. Söderlind, "Theoretical and computational aspects of partitioning in the numerical integration of stiff differential systems," Report 8115, Royal Institute of Technology, Stockholm, 1981.

    Google Scholar 

  33. A. B. Vasil’eva and V. F. Butuzov, Singularly Perturbed Equations in the Critical Case, Moscow State University, 1978.

    Google Scholar 

  34. W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York, 1965.

    MATH  Google Scholar 

  35. W. Wasow, "Topics in the theory of linear ordinary differential equations having singularities with respect to a parameter," Institut de recherche mathématique avancée, Strasbourg, 1978.

    MATH  Google Scholar 

  36. D. S. Watkins, "An initialization program for separably stiff systems," SIAM J. Sci. Stat. Comput., to appear.

    Google Scholar 

  37. R. Weiss, "An analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems," preprint, Technische Universitat Wien, 1982.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12181, Troy, New York, USA

    Robert E. O’Malley Jr.

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  1. Robert E. O’Malley Jr.
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F. Verhulst

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© 1983 Springer-Verlag

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O’Malley, R.E. (1983). Slow/fast decoupling for linear boundary value problems. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062370

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  • DOI: https://doi.org/10.1007/BFb0062370

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12286-9

  • Online ISBN: 978-3-540-39612-3

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