{"id":"W4379162573","doi":"10.1016/j.cam.2023.115378","title":"Numerical solution of two-dimensional weakly singular Volterra integral equations of the first kind via bivariate rational approximants","year":2023,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Mathematical analysis; Laplace transform; Volterra integral equation; Singularity; Integral equation; Singular integral; Asymptotic expansion; Series (stratigraphy); Bivariate analysis; Series expansion; Convergence (economics); Algebraic equation; Padé approximant; Algebraic number; Nonlinear system","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0008962862,0.0004860545,0.001089339,0.0006187995,0.0004585344,0.001355364,0.000667022,0.001102558,0.0009541743],"category_scores_gemma":[0.002635126,0.0002758016,0.000477584,0.0004546146,0.001163581,0.0007896259,0.0009333667,0.0009878098,0.0001532245],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005899826,"about_ca_system_score_gemma":0.0006558198,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004260773,"about_ca_topic_score_gemma":0.002111466,"domain_scores_codex":[0.9998103,0.00008430854,0.00001019368,0.00001281179,0.00005159388,0.00003082224],"domain_scores_gemma":[0.9993058,0.000396601,0.00006956599,0.00004920235,0.0001245524,0.00005416709],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0002446465,0.0001416316,0.001623102,0.0001097773,0.00006109143,0.0002081254,0.0002331507,0.9123944,0.008641485,0.06209404,0.0002652545,0.01398329],"study_design_scores_gemma":[0.000006137783,0.00001045396,0.00005086254,0.000003620567,0.00000336748,0.000006967666,0.00001271667,0.9984289,0.0003598515,0.001025281,0.00008863879,0.000003116142],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5577531,0.0007140451,0.4287636,0.0004366898,0.0002097259,0.00005663695,0.00004840143,0.0002713822,0.01174643],"genre_scores_gemma":[0.9619791,0.0002025318,0.03581418,0.00003139003,0.00002482623,0.00002663222,0.00002288863,0.00003193548,0.001866427],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004260773,"threshold_uncertainty_score":0.008471966,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04724576061583368,"score_gpt":0.3012820263820056,"score_spread":0.2540362657661719,"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."}}