A Sparse Differential Algebraic Equation (DAE) and Stiff Ordinary Differential Equation (ODE) Solver in Maple
Bibliographic record
Abstract
This paper implements efficient numerical methods in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs) and stiff Ordinary Differential Equations (ODEs) systems. Single-step methods (like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), Radau IIA (Rad) methods, TRBDF2, TRX2) and backward-difference formula of order 2 are implemented with adaptive time-stepping methods in Maple to solve index-1 nonlinear DAEs. Maple’s robust and efficient ability to search within a list/set is exploited to identify the sparsity pattern and automatically calculate the analytic Jacobian. The algorithm and implementation are robust and efficient for index-1 DAE problems and scale well for finite difference/finite element discretization of two-dimensional models with system size up to 10,000 nonlinear DAEs and solve the same in a few seconds. The computational efficiency of the proposed algorithm (provided as an open-access code) compares favorably with the commercial solver gPROMs, one of the most commonly used sparse DAE solvers in the industry.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.004 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".