Implicit Extensions of an Explicit Multirate Runge-Kutta Scheme

Emil M. Constantinescu

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Implicit Extensions of an Explicit Multirate Runge-Kutta Scheme

Emil M. Constantinescu

Numerical Analysis · Submitted 20 Dec 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,475 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.39 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable for time-stepping adaptive mesh refinement PDE discretizations with different degrees of stiffness. A numerical example with an advection-diffusion problem illustrates the new method's properties.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods.	contribution 1.00	0.94	0.51	asserted 1.00
s1	We develop extensions of order one and two with different stability properties on the implicit side.	contribution 0.92	0.95	0.16	asserted 1.00
s2	The method is suitable for time-stepping adaptive mesh refinement PDE discretizations with different degrees of stiffness.	interpretation 0.50	0.35	0.14	asserted 0.97
s3	A numerical example with an advection-diffusion problem illustrates the new method's properties.	method 0.64	0.92	0.08	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.97.

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arXiv listing abstract v1

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P abstract

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S sections
T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable for time-stepping adaptive mesh refinement PDE discretizations with different degrees of stiffness. A numerical example with an advection-diffusion problem illustrates the new method's properties.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 1 paper

The reader is referred to [ref] and a recent algorithmic presentation in [ref] for a more in-depth description of these methods.

Entropy-Preserving and Entropy-Stable Relaxation IMEX and Multirate Time-Stepping Methods · MPRK Methods · 0.81

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