{"id":"W2009402935","doi":"10.1007/s00211-009-0245-3","title":"Error analysis of variational integrators of unconstrained Lagrangian systems","year":2009,"lang":"de","type":"article","venue":"Numerische Mathematik","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":47,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Variational integrator; Mathematics; Variational analysis; Integrator; Singularity; Lagrangian; Applied mathematics; Symmetry (geometry); Variational method; Numerical analysis; Error analysis; Variational principle; Order (exchange); Mathematical analysis; Luke's variational principle; Hamilton's principle; Classical mechanics; Equations of motion; Geometry; Computer science; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004276212,0.001038189,0.001329753,0.001383923,0.0007402632,0.002500192,0.001625005,0.002205417,0.001684473],"category_scores_gemma":[0.01092467,0.0006816442,0.0006642856,0.0006657182,0.002102129,0.001845228,0.003230749,0.001420287,0.0001835121],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001591155,"about_ca_system_score_gemma":0.001819346,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.009267969,"about_ca_topic_score_gemma":0.005450241,"domain_scores_codex":[0.9991056,0.0003991809,0.00005966192,0.00009000001,0.0002643406,0.00008123026],"domain_scores_gemma":[0.9957622,0.002501366,0.0004242404,0.0002303141,0.0008348942,0.0002470278],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001858348,0.00009903206,0.001167463,0.0001448406,0.00008169877,0.00009109438,0.0002025322,0.8401546,0.002772118,0.1416398,0.0005518142,0.01290931],"study_design_scores_gemma":[0.000005257705,0.00001501128,0.00006345018,0.000006453336,0.000003435234,0.000004764067,0.000008484126,0.9931525,0.0001729218,0.006429373,0.0001334777,0.000004942681],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1623841,0.001464629,0.8235765,0.0007951339,0.0002923828,0.0001048432,0.00008531233,0.0001318599,0.01116526],"genre_scores_gemma":[0.9039997,0.0005921503,0.08041863,0.0001311098,0.0001206857,0.0001511465,0.0001594499,0.0001919582,0.01423511],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009267969,"threshold_uncertainty_score":0.02261508,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04763449942194269,"score_gpt":0.3404475544683849,"score_spread":0.2928130550464422,"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."}}