Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Advection-diffusion-reaction (ADR) models describe transport mechanisms in fluid or solid media. They are often formulated as partial differential equations that are spatially discretized into systems of ordinary differential equations (ODEs) in time for numerical resolution. This paper investigates the performance of variable stepsize, semi-implicit, backward differentiation formula (VSSBDF) methods of up to fourth order for solving ADR models employing two different implicit-explicit splitting approaches: a physics-based splitting and a splitting based on a dynamic linearization of the resulting system of ODEs, called jacobian splitting in this paper. We develop an adaptive time-stepping and error control algorithm for VSSBDF methods up to fourth order based on a step-doubling refinement technique using estimates of the local truncation errors. Through a systematic comparison between physics-based and Jacobian splitting across six ADR test models, we evaluate the performance based on CPU times and corresponding accuracy. Our findings demonstrate the general superiority of Jacobian splitting in several experiments.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it