Modern convergence theory for stiff initial-value problems

Journal of Computational and Applied Mathematics

Volumn 45, Issue 1-2, 1993, Pages 5-16

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

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

convergence; stability; Stiff differential equations

Indexed keywords

EID: 0038915819     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(93)90260-I     Document Type: Article

References (36)

1. On the error structure of the implicit Euler scheme applied to stiff systems of differential equations
2. On error structures and extrapolation for stiff systems, with application in the method of lines
3. Asymptotic Expansions of the Global Discretization Error for Stiff Problems
4. Asymptotic error expansions for stiff equations: applications
5. A note on convergence concepts for stiff problems
6. An extension of B-convergence for Runge—Kutta methods
7. Asymptotic error expansions for stiff equations: the implicit Euler scheme
8. Stability Criteria for Implicit Runge–Kutta Methods
9. A stability property of implicit Runge—Kutta methods
10. Sur la B-stabilité des méthodes de Runge—Kutta
11. Stability and error bounds in the numerical integration of ordinary differential equations
12. A special stability problem for linear multistep methods
13. Error analysis for a class of methods for stiff nonlinear initial value problems
14. G-stability is equivalent to A-stability
15. Einseitige Lipschitzbedingungen für gewöhnliche Differentialgleichunge
16. The Concept of B-Convergence
17. Stability properties of implicit Runge—Kutta methods
18. Order results for implicit Runge—Kutta methods applied to stiff systems
19. B-convergence: A survey
20. Extrapolation at stiff differential equations
21. Error of Runge—Kutta methods for stiff problems studied via differential algebraic equations
22. Contractivity of Runge—Kutta methods
23. Méthodes multipas pour des équations paraboliques non linéaires
24. On the resolvent condition in the Kreiss matrix theorem
25. On the convergence of multistep methods for nonlinear stiff differential equations
26. On resolvent conditions and stability estimates
27. On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations
28. Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues
29. Stability and convergence at the PDE/stiff ODE interface
30. Contractivity in the numerical solution of initial value problems
31. Asymptotic expansions for the error of discretization algorithms for nonlinear functional equations
32. Asymptotic expansions of the global error for the implicit midpoint rule (stiff case)
33. A note on unconditionally stable linear multistep mehtods