An almost L-stable BDF-type method for the numerical solution of stiff ODEs arising from the method of lines

Numerical Methods for Partial Differential Equations

Volumn 23, Issue 5, 2007, Pages 1110-1121

  Ramos, Higinio ^a   Vigo Agular, Jesús ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

A( ) stability; Almost L stability; BDF type methods; Method of lines; Stiff initial value problems

Indexed keywords

EID: 34548539990     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20212     Document Type: Article

References (23)

1. 1 J. M. Phillips and P. J. Taylor, Theory and Applications of Numerical Analysis, Academic Press, London, 1973.
2. 2 C. F. Curtiss and J. O. Hirschfelder, Integration of stiff equations, Proc Nat Acd Sci 38 ( 1952), 235–243.
3. 3 J. D. Lambert, Numerical methods for ordinary differential systems, John Wiley, England, 1991.
4. 4 J. C. Butcher and N. Rattenbury, ARK methods for stiff problems, Appl Numer Math 53 ( 2005), 165–181.
5. 5 J. R. Cash, On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae, Numer Math 34 ( 1980), 235–246.
6. 6 J. R. Cash and Y. Psihoyios, The MOL solution of time dependent partial differential equations, Computers Math Appl 31 ( 1996), 69–78.
7. 7 C. Fredebeul, A‐BDF: a generalization of the backward differentiation formulae, SIAM J Numer Anal 35 (5) ( 1998), 1917–1938.
8. 8 N. Guzel and M. Bayram, On the numerical solution of stiff systems, Appl Math Comp 170 ( 2005), 230–236.
9. 9 E. Hairer and G. Wanner, Stiff differential equations solved by Radau methods, J Comp Appl Math 111 ( 1999), 93–111.
10. 10 M. M. Stabrowski, An efficient algorithm for solving stiff ordinary differential equations, Simul Pract Theor 5 ( 1997), 333–344.
11. 11 D. L. Richardson, D. Schmidt, and J. Mitchell, “ Improved Chebysehv methods for the numerical integration of first‐order differential equations,” AAS/AIAA Space Flight Mechanics Meeting, Paper No. 98‐208, Monterey, CA, 1998.
12. 12 J. Vigo‐Aguiar and H. Ramos, Dissipative Chebyshev exponential‐fitted methods for numerical solution of second‐order differential equations, J Comp Appl Math 158 ( 2003), 187–211.
13. 13 J. Vigo‐Aguiar and D. L. Richardson, Modification of the Richardson‐Panowsky methods for precise integration of satellite orbits, Comput Math Appl 45 ( 2003), 25–36.
14. 14 E. Hairer, S. P. Norsett, and G. Wanner, Solving ordinary differential equations I, Springer, Berlin, 1993.
15. 15 P. Henrici, Discrete variable methods in ordinary differential equations, John Wiley, New York, 1962.
16. 16 J. Villadsen and M. L. Michelsen, Solution of differential equation models by polynomial approximation, Prentice‐Hall, Englewod Cliffs, NJ, 1978.
17. 17 L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London, 1968.
18. 18 E. Hairer and G. Wanner, Solving ordinary differential equations II. Stiff and differential‐algebraic problems, Springer, Berlin, 1996.
19. 19 W. E. Schiesser, The numerical method of lines, Academic Press, New York, 1991.
20. 20 J. R. Cash, Two new finite difference schemes for parabolic equations, SIAM J Numer Anal 21 ( 1984), 433–445.
21. 21 M. T. Diamantakis, The NUMOL solution of time‐dependent PDEs using DESI Runge‐Kutta Formulae, Appl Numer Math 17 ( 1995), 235–249.
22. 22 A. Mazzia and F. Mazzia, High‐order transverse schemes for the numerical solution of PDEs, J Comp Appl Math 82 ( 1997), 299–311.
23. 23 L. F. Shampine, ODE solvers and the method of lines, Numer Methods Partial Differential Eq 10 ( 1994), 739–755.