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Linear multistep methods applied to stiff initial value problems—A survey

✍ Scribed by G. Kirlinger

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
766 KB
Volume
40
Category
Article
ISSN
0895-7177

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✦ Synopsis

The numerical approximation of solutions of differential equations has been and continues to be one of the principal concerns of numerical analysis. Linear multistep methods and, in particular, backward differentiation formulae (BDFs) are frequently used for the numerical integration of stiff initial value problems. Such stiff problems appear in a variety of applications.

While the intuitive meaning of stiffness is clear to all specialists, there has been much controversy about its correct mathematical definition. We present a historical development of the concept of stiffness. A survey of convergence results for special classes of stiff problems based on these different concepts of stiffness is given, e.g., for linear, stiff systems, problems in singular perturbation form, nonautonomous stiff systems, and rather general nonlinear stiff problems. Different approaches proving convergence of linear multistep methods applied to stiff initial value problems are introduced. It is further indicated that the corresponding proofs for singular perturbation problems are compatible with a nonlinear transformation and thus convergence of a quite general class of nonlinear problems seems to be covered.

📜 SIMILAR VOLUMES

Convergence of BDFs applied to nonlinear
Convergence of BDFs applied to nonlinear stiff initial value problems
✍ G. Kirlinger 📂 Article 📅 2002 🏛 John Wiley and Sons ⚖ 104 KB

## Convergence of BDFs applied to nonlinear stiff initial value problems We present bounds for the global errors of backward differentiation formulas (BDFs) applied to non-autonomous stiff problems y = A(t)y + Φ(t) and outline the analysis for convergence of BDFs applied to rather general nonlinea

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