A BVP solver that controls residual and error

Journal of Numerical Analysis, Industrial and Applied Mathematics

Volumn 3, Issue 1-2, 2008, Pages 27-41

  Kierzenka, J ^a   Shampine, L F ^b  

^a MATHWORKS INC   (United States)

^b SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

Boundary value problems; Collocation; Error control; Ordinary differential equations; Residual

Indexed keywords

EID: 58249086655     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. ACDC, http://www.ma.ic.ac.uk/~jcash/BVP_software/readme.php
2. U.M. Ascher, J. Christiansen, and R.D. Russell, Collocation software for boundary value ODEs, ACM Trans. Math. Softw. 7 209-222(1981).
3. U.M. Ascher, R.M.M. Mattheij, and R.D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, SIAM, Philadelphia, 1995.
4. U.M. Ascher and R.D. Russell, Reformulation of boundary value problems into \standard" form, SIAM Rev. 23 238-254(1981).
5. Z. Bashir-Ali, J.R. Cash, and H.H.M. Silva, Lobatto deferred correction for stiff two-point boundary value problems, Comp. & Maths. with Applics. 36 59-70(1998).
6. J.R. Cash and H.H.M. Silva, On the numerical solution of a class of singular two-point BVPs, J. Comput. Appl. Math. 45 91-102(1993).
7. T.A. Davis, UMFPACK Version 4.6 User Guide, Dept. Computer and Information Science and Engineering, Univ. of Florida, Gainesville, FL, 2002.
8. K. Dekker and J.G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, North-Holland, Amsterdam, 1984.
9. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II Stiff and Differential-Algebraic Problems, 2nd ed., Springer, New York, 1996.
10. J. Kierzenka and L.F. Shampine, A BVP solver based on residual control and the Matlab PSE, ACM Trans. Math. Softw. 27 299-316(2001).
11. Maple, Maplesoft, 615 Kumpf Dr., Waterloo, CA, N2V 1K8
12. Matlab, The MathWorks, Inc., 3 Apple Hill Dr., Natick, MA 01760.
13. R.D. Russell and J. Christiansen, Adaptive mesh selection strategies for solving boundary value problems, SIAM J. Numer. Anal. 14 59-80(1978).
14. L.F. Shampine, Singular boundary value problems for ODEs, Appl. Math. and Comp. 138 99-112(2003).
15. L.F. Shampine, Solving ODEs and DDEs with Residual Control, Appl. Numer. Math 52 113-127(2005).
16. L.F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with Matlab, Cambridge Univ. Press, New York, 2003.
17. L.F. Shampine, P.H. Muir, and H. Xu, A User-friendly Fortran BVP solver, JNAIAM, to appear. The paper and programs are available at http://cs.stmarys.ca/~muir/BVP_SOLVER_Webpage.shtml
18. L.F. Shampine, M.W. Reichelt, and J. Kierzenka, Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c. The tutorial and programs are available at http://www.mathworks.com/bvp_tutorial
19. S.J. Wright, A collection of problems for which Gaussian elimination with partial pivoting is unstable, SIAM J. Sci. Comput. 14 231-238(1993).