High-order finite difference schemes for the solution of second-order BVPs

Journal of Computational and Applied Mathematics

Volumn 176, Issue 1, 2005, Pages 59-76

  Amodio, Pierluigi ^a   Sgura, Ivonne ^b  

^a UNIVERSITY OF BARI   (Italy)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

Boundary value methods; Conditioning analysis; Finite difference schemes; Two point boundary value problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION;

BOUNDARY VALUE METHODS; CONDITIONING ANALYSIS; FINITE DIFFERENCE SCHEMES; TWO-POINT BOUNDARY VALUE PROBLEMS;

FINITE DIFFERENCE METHOD;

EID: 27744495163     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.07.008     Document Type: Article

References (19)

1. L. Aceto, and D. Trigiante On the A-stable methods in the GBDF class Nonlinear Anal. Real World Appl. 3 1 2002 9 23
2. P. Amodio, and L. Brugnano The conditioning of Toeplitz band matrices Math. Comput. Modelling 23 10 1996 29 42
3. P. Amodio, F. Iavernaro, Symmetric boundary value methods for second order boundary value problems, preprint, Dipartimento di Matematica, Università di Bari, 2003.
4. U.M. Ascher, R.M.M. Mattheij, R.D. Russell, Numerical Solution of Boundary Value Problems for ODEs, Classics in Applied Mathematics, vol. 13, SIAM, Philadelphia,1995.
5. L. Brugnano, and D. Trigiante Solving ODEs by Linear Multistep Initial and Boundary Value Methods 1998 Gordon and Breach Amsterdam
6. J. Cash, BVP software web page, http://www.ma.ic.ac.uk/ ∼ jcash/BVP_software/readme.html.
7. J.R. Cash, and M.H. Wright A deferred correction method for nonlinear two-point boundary value problems implementation and numerical evaluation SIAM J. Sci. Statist. Comput. 12 1991 971 989
8. W.H. Enright, and P.H. Muir Runge-Kutta software with defect control for boundary value ODEs SIAM J. Sci. Comput. 17 1996 479 497
9. B. Fornberg, and M. Ghrist Spatial finite difference approximations for wave-type equations SIAM J. Numer. Anal. 37 1 1999 105 130
10. D. Greenspan, and V. Casulli Numerical Analysis for Applied Mathematics 1988 Science and Engineering Perseus Books Eds., MA
11. B. Gustafsson, H.O. Kreiss, and J. Oliger Time Dependent Problems and Difference Methods 1995 Wiley New York
12. F. Iavernaro, and D. Trigiante Preconditioning and conditioning of systems arising from boundary value methods Nonlinear Dynamic System Theory 1 2001 59 80
13. F. Mazzia, BVP Software web page, http://www.dm.uniba.it/ ∼ mazzia.
14. F. Mazzia, and I. Sgura Numerical approximation of nonlinear BVPs by means of BVMs Appl. Numer. Math. 42 1-3 2002 337 352
15. F. Mazzia, and D. Trigiante Numerical methods for second order singular perturbation problems Comput. Math. Appl. 23 11 1992 81 89
16. A. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, Springer Series in Computational Mathematics, vol. 23, Springer, Berlin, 1994.
17. I. Sgura, The method of lines coupled with BVMs for the numerical approximation of elliptic PDEs, preprint 1/2003, Dipartimento di Matematica, Università di Lecce, 2003.
18. L.F. Shampine, M.W. Reichelt, J. Kierzenka, Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c, available at ftp://ftp.mathworks.com/pub/doc/papers/bvp/.
19. T. Styś O (τ 2 + h 4 ) finite difference scheme for decoupled system of two quasilinear parabolic equations J. Comput. Appl. Math. 66 1-2 1996 485 496