Numerical Solutions for Fuzzy Stochastic Ordinary Differential Equations Using Heun’s Method with a Dual-Wiener Process Framework
Bibliographic record
Abstract
This analysis aims to adapt the Heun's numerical method integrated with a dual-Wiener process framework to solve fuzzy stochastic differential equations (FSDEs) by processing challenges faced by randomness and uncertainty.FSDEs incorporate stochastic processes with fuzzy parameters, such as triangular and trapezoidal fuzzy numbers, to model uncertainties arising from incomplete or imprecise data.The modified Heun's method is a predictor-corrector scheme designed to enhance accuracy and computational stability, outperforming traditional methods like Euler-Maruyama.The main contributions include the combining of fuzzy arithmetic into stochastic models and the use of dual-Wiener processes to account for complex uncertainties.The study demonstrates theoretical convergence under fuzzy and stochastic conditions and validates its findings through numerical simulations.Results confirm the method's strong and weak convergence, as well as its robustness in tackling FSDEs across applications in finance, engineering, and environmental modeling.Comparative analysis highlights significant error reduction, particularly in cases with larger sample sizes, underscoring the method's efficacy.Our study bridges openings in numerical solutions for FSDEs by presenting an applicable and efficient approach for solving problems in systems with random and fuzzy parameters.Future work may focus on extending the methodology to higher-dimensional systems and integrating machine learning techniques to enhance performance further.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".