Numerical Solutions for Fuzzy Stochastic Ordinary Differential Equations Using Heun’s Method with a Dual-Wiener Process Framework
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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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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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