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Stability analysis of the BDF slowest-first multirate methods. (English) Zbl 1125.65066

The authors discuss the stability of numerical schemes for initial value problems in ordinary differential equations or differential-algebraic equations which feature latency or a multirate behavior. To accomodate for this property, multirate methods integrate the different subsystems with different time-stepping or even different discretization schemes. The present paper studies the so-called slow-fast version of backward differentiation formula (BDF) schemes for step size control reasons. Several stability results are proven provided that the subsystems are sufficiently decoupled, stable and solvable.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34E13 Multiple scale methods for ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L80 Numerical methods for differential-algebraic equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

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