A collocation code for singular boundary value problems in ordinary differential equations

Numerical Algorithms

Volumn 33, Issue 1-4, 2003, Pages 27-39

  Auzinger, Winfried ^a   Kneisl, Günter ^a   Koch, Othmar ^a   Weinmüller, Ewa ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Collocation; Singular boundary value problems

Indexed keywords

EID: 0041375531     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025531130904     Document Type: Conference Paper

References (17)

1. U. Ascher, R. Mattheij and R. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, NJ, 1988).
2. W. Auzinger, G. Kneisl, O. Koch and E. Weinmüller, SBVP 1.0 - A MATLAB solver for singular boundary value problems, Institute for Appl. Math. and Numer. Anal., Vienna University of Technology, Austria (2002); also available as ANUM Preprint Nr. 2/02 at http://www.math.tuwien.ac.at/̃inst115/preprints.htm.
3. W. Auzinger, G. Kneisl, O. Koch and E. Weinmüller, A solution routine for singular boundary value problems, Technical Report, ANUM Preprint Nr. 1/02, Institute for Appl. Math. and Numer. Anal., Vienna University of Technology, Austria (2002); available at http: //www.math. tuwien.ac.at/̃inst115/preprints.htm.
4. W. Auzinger, O. Koch, W. Polster and E. Weinmüller, Ein Algorithmus zur Gittersteuerung bei Kollokationsverfahren für singuläre Randwertprobleme, Technical Report ANUM Preprint Nr. 21/01, Institute for Appl. Math. and Numer. Anal., Vienna University of Technology, Austria (2001); available at http://www.math.tuwien.ac.at/̃inst115/preprints.htm.
5. W. Auzinger, O. Koch and E. Weinmüller, Efficient collocation schemes for singular boundary value problems, Numer. Algorithms 31 (2002) 5-25.
6. W. Auzinger, P. Kofler and E. Weinmüller, Steuerungsmaßnahmen bei der numerischen Lösung singulärer Anfangswertaufgaben, Technical Report Nr. 124/98, Institute for Appl. Math. and Numer. Anal., Vienna University of Technology (1998); available at http: //www.math.tuwien.ac.at/̃ewa/abstrc90.html#steuer.
7. R. Frank and C. Überhuber, Iterated defect correction for differential equations, Part I: Theoretical results, Computing 20 (1978) 207-228.
8. F. Frommlet and E. Weinmüller, Asymptotic error expansions for singular boundary value problems, Math. Models Methods Appl. Sci. 11 (2001) 71-85.
9. F. d. Hoog and R. Weiss, Difference methods for boundary value problems with a singularity of the first kind, SIAM J. Numer. Anal. 13 (1976) 775-813.
10. F. d. Hoog and R. Weiss, Collocation methods for singular boundary value problems, SIAM J. Numer. Anal. 15 (1978) 198-217.
11. O. Koch and E. Weinmüller, The convergence of shooting methods for singular boundary value problems, Math. Comp. 72 (2003) 289-305.
12. O. Koch and E. Weinmüller, Iterated defect correction for the solution of singular initial value problems, SIAM J. Numer. Anal. 38(6) (2001) 1784-1799.
13. L. Shampine, J. Kierzenka and M. Reichelt, Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c (2000); available at ftp://ftp.mathworks.com/pub/doc/papers/bvp/.
14. H. J. Stetter, The defect correction principle and discretization methods, Numer. Math. 29 (1978) 425-443.
15. E. Weinmüller, Collocation for singular boundary value problems of second order, SIAM J. Numer. Anal. 23 (1986) 1062-1095.
16. E. Weinmüller, On the numerical solution of singular boundary value problems of second order by a difference method, Math. Comp. 46 (1986) 93-117.
17. P. Zadunaisky, On the estimation of errors propagated in the numerical integration of ODEs, Numer. Math. 27 (1976) 21-39.