Numerical Solution of Asymptotic Two-Point Boundary Value Problems with Application to the Swirling Flow over a Plane Disk

  • Hans Josef Pesch
  • Peter Rentrop
Conference paper


A technique is presented for the numerical solution of asymptotic two-point boundary value problems. Thereby the boundary layer part of the solution, defined over a finite interval, is splitted from the asymptotic part of the solution. By a linearization technique one obtains surrogate boundary conditions so that the infinite problem can be efficiently approximated by a finite problem. This allows the convenient application of standard software for the solution of two-point boundary value problems. As a main example, the swirling flow of a viscous incompressible fluid over an infinite plane disk is investigated. Limitations of the procedure are discussed.


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  1. [1.]
    Ascher, U.; Russel, R. D.: Reformulation of Boundary Value Problems into `Standard Form’. SIAM Review 23 (1981) 238–254MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2.]
    Baindl, G.: Numerische Berechnung asymptotischer Randwertprobleme der Hydromechanik mit Hilfe der Mehrzielmethode. Department of Mathematics, Munich University of Technology: Diploma Thesis 1983.Google Scholar
  3. [3.]
    Deuflhard, P.; Bader, G.: Multiple Shooting Techniques Revisited. In: Deuflhard, P.; Hairer, E. (eds.): Numerical Treatment of Inverse Problems in Differential and Integral Equations. Progress in Scientific Computing 2 (1983) 74–94CrossRefGoogle Scholar
  4. [4.]
    Deuflhard, P.; Pesch, H. J.; Rentrop, P.: A Modified Continuation Method for the Numerical Solution of Nonlinear Two-Point Boundary Value Problems by Shooting Techniques. Numer. Math. 26 (1976) 327–343MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5.]
    Diekhoff, H. J.; Lory, P.; Oberle, H. J.; Pesch, H. J.; Rentrop, P.; Seydel, R.: Comparing Routines for the Numerical Solution of Initial Value Problems of Ordinary Differential Equations in Multiple Shooting. Numer. Math. 27 (1977) 449–469MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6.]
    Lentini, M.; Keller, H. B.: Boundary Value Problems Over Semi-Infinite Intervals and Their Numerical Solution. SIAM J. Numer. Anal. 17 (1980) 577–604MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7.]
    Markowich, P. A.: Analysis of Boundary Value Problems on Infinite Intervals. SIAM J. Math. Anal. 14 (1983) 11–37 MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8.]
    Mattheij, R. M. M.: Decoupling and Stability of Algorithms for Boundary Value Problems. SIAM Review 27 (1985) 1–44MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9.]
    Pesch, H. J.; Rentrop, P.: Numerical Solution of the Flow Between Two Counter-Rotating Infinite Plane Disks by Multiple Shooting. ZAMM 58 (1978) 23–28MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10.]
    Stenger, F.: Numerical Methods Based on Whittaker Cardinal or SINC Functions.SIAM Review 23 (1981) 165–224MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11.]
    Stoer, J.; Bulirsch, R.: Introduction to Numerical Analysis. Berlin, New York, Heidelberg: Springer 1980.Google Scholar
  12. [12.]
    Strauss, W.; Vazquez, L.: Numerical Solution of a Nonlinear Klein-Gordon Equation. J. Comp. Phys. 28 (1978) 271–278MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13.]
    Troesch, B. A.: The Limiting Vortex in the Similarity Solution of a Swirling Flow. Appl. Math. & Comp. 6 (1980) 133–144MathSciNetzbMATHGoogle Scholar

Copyright information

© B. G. Teubner Stuttgart 1989

Authors and Affiliations

  • Hans Josef Pesch
    • 1
  • Peter Rentrop
    • 1
  1. 1.Mathematisches InstitutTechnische Universität MünchenMünchen 2Germany

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