Extending convergence theory for nonlinear stiff problems part I

BIT Numerical Mathematics

Volumn 36, Issue 4, 1996, Pages 635-652

  Auzinger, W ^a   Frank, R ^a   Kirlinger, G ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Convergence; Stiff differential equations

Indexed keywords

EID: 1542610661     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01733784     Document Type: Article

References (12)

1. W. Auzinger, R. Frank, and G. Kirlinger, Extending convergence theory for non-linear stiff problems. Part I, Report 116/94, Institute for Applied and Numerical Mathematics, Vienna University of Technology (extended version of the present paper).
2. W. Auzinger, R. Frank, and G. Kirlinger, A note on convergence concepts for stiff problems. Computing 44 (1990), pp. 197-208.
3. K. Dekker and J. G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, North-Holland, 1984.
4. R. Frank and C. W. Ueberhuber, Iterated defect-correction for the efficient solution of stiff systems of ordinary differential equations, BIT 17 (1977), pp. 146-159.
5. R. Frank, J. Schneid, and C. W. Ueberhuber, The concept of B-convergence, SIAM J. Numer. Anal. 18 (1981), pp. 753-780.
6. R. Frank, J. Schneid, and C. W. Ueberhuber, Stability properties of implicit Runge-Kutta methods, SIAM J. Numer. Anal. 22 (1985), pp. 497-515.
7. R. Frank, J. Schneid, and C. W. Ueberhuber, Order results for implicit Runge-Kutta methods applied to stiff systems, SIAM J. Numer. Anal. 22 (1985), pp. 515-534.
8. E. Hairer, C. Lubich, M. Roche, Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations, BIT 28 (1988), pp. 678-700.
9. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer, 1991.
10. Ch. Lubich, On the convergence of multistep methods for nonlinear stiff differential equations, Numer. Math. 58 (1991), pp. 839-853; Erratum, 61 (1992), pp. 277-279.
11. K. Nipp and D. Stoffer, Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type, Numer. Math., 70 (1995), pp. 245-257.
12. A. Prothero and A. Robinson, On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations, Math. Comp. 28 (1974), pp. 145-162.