{"id":"W4401954371","doi":"10.18280/mmep.110815","title":"Development and Analysis of Embedded Explicit Runge-Kutta Methods for Directly Solving Special Fifth-Order Quasi-Linear Ordinary Differential Equations","year":2024,"lang":"en","type":"article","venue":"Mathematical Modelling and Engineering Problems","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Runge–Kutta methods; Linear multistep method; Ordinary differential equation; Mathematics; Applied mathematics; Linear differential equation; Differential equation; Order (exchange); Backward differentiation formula; Mathematical analysis; Differential algebraic equation","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.00084957,0.0003110691,0.0008044589,0.0004472547,0.0001325469,0.0001080192,0.0001212316,0.0001423328,0.00007342678],"category_scores_gemma":[0.0006314844,0.0002689692,0.0001942182,0.0006659022,0.00004253484,0.0001086435,0.00009835821,0.0002099195,0.000002115612],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000395137,"about_ca_system_score_gemma":0.00003163921,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003891339,"about_ca_topic_score_gemma":0.000001016877,"domain_scores_codex":[0.9980865,0.00006344749,0.0008414069,0.0004286883,0.0002216385,0.0003583548],"domain_scores_gemma":[0.9960359,0.003381401,0.00009687916,0.0002406935,0.00009599853,0.000149096],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00004065856,0.0006873655,0.000004475844,0.00927206,0.004219767,0.000002209414,0.02221702,0.148203,0.01553812,0.7075544,0.00001537954,0.09224554],"study_design_scores_gemma":[0.0001431478,0.0000425643,0.000002488419,0.0003168466,0.001104776,0.000001590569,0.00005327001,0.8275244,0.0006840221,0.1696415,0.0002356031,0.0002498534],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.05009202,0.0003229027,0.9486648,0.00004091523,0.0001600049,0.0004522698,0.00001786363,0.0002012311,0.00004795315],"genre_scores_gemma":[0.04551169,0.00002047319,0.9538314,0.000002459955,0.0001328563,0.0002061924,0.00002562538,0.00006893336,0.0002003274],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.6793214,"threshold_uncertainty_score":0.9999763,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09972423485624982,"score_gpt":0.364344221897861,"score_spread":0.2646199870416112,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}