{"id":"W3208001668","doi":"10.5539/jmr.v13n6p10","title":"Linearized Homotopy Perturbation Method for Two Nonlinear Problems of Duffing Equations","year":2021,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Duffing equation; Homotopy analysis method; Mathematical analysis; Nonlinear system; Differential equation; Linearization; Homotopy; Applied mathematics","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.005805436,0.0001371634,0.0005153476,0.0005900124,0.0002826467,0.00009340936,0.0003098607,0.0001134069,0.0002184784],"category_scores_gemma":[0.02676382,0.0001201646,0.0003467037,0.0007672744,0.00008682202,0.0002527278,0.0001001947,0.0005763842,0.00001090132],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001839012,"about_ca_system_score_gemma":0.0008360358,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001146109,"about_ca_topic_score_gemma":0.00003936724,"domain_scores_codex":[0.9963056,0.0004609175,0.001378826,0.0001622846,0.001379858,0.0003125512],"domain_scores_gemma":[0.9794396,0.01302657,0.0008050929,0.0003771483,0.006234747,0.0001168584],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00007307828,0.004231181,0.00001512352,0.001795201,0.0005627546,0.000009884563,0.003696246,0.004044203,0.1612084,0.8192036,0.002153602,0.003006791],"study_design_scores_gemma":[0.001367416,0.0001862966,0.0000100956,0.0004485347,0.0001343952,0.0000717487,0.001150387,0.3875136,0.01928967,0.5889865,0.0007306922,0.0001106714],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01230848,0.0001541965,0.9843158,0.001514973,0.0001787371,0.0005633479,0.00004336784,0.00001445483,0.0009066459],"genre_scores_gemma":[0.04332933,0.00004713807,0.9542104,0.00001033688,0.0003225214,0.00005402204,0.00001999525,0.00004468107,0.001961576],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3834694,"threshold_uncertainty_score":0.9814342,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3315947804370815,"score_gpt":0.5202142636512854,"score_spread":0.188619483214204,"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."}}