Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On theoretical upper limits for valid timesteps of implicit ODE methods   Implicit methods for the numerical solution of initial-value problems may
admit multiple solutions at any given time step. Accordingly, their nonlinear
solvers may converge to any of these solutions. Below a critical timestep,
exactly one of the solutions (the consistent solution) occurs on a solution
branch (the principal branch) that can be continuously and monotonically
continued back to zero timestep.
  Standard step-size control can promote convergence to consistent solutions by
adjusting the timestep to maintain an error estimate below a given tolerance.
However, simulations for symplectic systems or large physical systems are often
run with constant timesteps and are thus more susceptible to convergence to
inconsistent solutions. Because simulations cannot be reliably continued from
inconsistent solutions, the critical timestep is a theoretical upper bound for
valid timesteps.

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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci