Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems

Applied Numerical Mathematics

Volumn 28, Issue 2-4, 1998, Pages 227-244

  Cash, J R ^a   Wright, R W ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Deferred correction; Interpolant; Two point boundary value problem

Indexed keywords

BOUNDARY VALUE PROBLEMS; ERROR CORRECTION; INTERPOLATION; NONLINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

ACDC CODE; DEFERRED CORRECTION; TWPBVP CODE;

RUNGE KUTTA METHODS;

EID: 0032182567     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00045-2     Document Type: Article

References (16)

1. U. Ascher, J. Christiansen and R.D. Russell, Collocation software for boundary value ODEs, ACM Trans. Math. Software 7 (1981) 209-222.
2. J.R. Cash, On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, Part 1: A survey and comparison of some one-step formulae, Comput. Math. Appl. 12a (1986) 1029-1048.
3. J.R. Cash, On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, Part 2: The development and analysis of highly stable deferred correction formulae, SIAM J. Numer. Anal. 24 (1988) 862-882.
4. J.R. Cash, A comparison of some global methods for solving two-point boundary value problems, Appl. Math. Comput. 31 (1989) 449-462.
5. J.R. Cash, G. Moore and R.W. Wright, An automatic continuation strategy for the solution of singularly perturbed linear two-point boundary value problems, J. Comput. Phys. 122 (1995) 266-279.
6. J.R. Cash, G. Moore and R.W. Wright, An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems, to appear.
7. J.R. Cash and A. Singhal, High order methods for the numerical solution of two-point boundary value problems, BIT 22 (1982) 184-199.
8. 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.
9. P.W. Hemker, A numerical study of stiff two-point boundary value problems, Mathematisch Centrum, Amsterdam (1977).
10. M. Lentini and V. Pereyra, An adaptive finite difference solver for nonlinear two-point boundary value problems with mild boundary layers, SIAM J. Numer. Anal. 14 (1977) 91-111.
11. P. Muir and B. Owren, Order barriers and characterisations for continuous mono-implicit Runge-Kutta schemes, Math. Comp. 61 (1993) 675-691.
12. B. Owren and M. Zennaro, Derivation of optimal explicit Runge-Kutta methods, SIAM J. Sci. Statist. Comput. 13 (1992) 1488-1501.
13. S. Pruess, Interpolation schemes for collocation solutions of two-point boundary value problems, SIAM J. Sci. Comput. 7 (1986) 322-333.
14. S. Pruess and H. Jin, A stable high order interpolation scheme for superconvergent data, SIAM J. Sci. Statist. Comput. 17 (1996) 714-724.
15. R.D. Skeel, A theoretical foundation for proving accuracy results for deferred corrections, SIAM J. Numer. Anal. 19 (1982) 171-196.
16. R. W. Wright, An automatic continuation strategy for the numerical solution of stiff two-point boundary value problems, Ph.D. Thesis, Imperial College, University of London (1995).