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{
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{
            
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  "author": "D\u00f6rich, Benjamin",
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  "author": "D\u00f6rich, Benjamin",
            
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  "author_email": "",
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  "author_email": "",
            
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  "creator_user_id": "17755db4-395a-4b3b-ac09-e8e3484ca700",
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  "creator_user_id": "17755db4-395a-4b3b-ac09-e8e3484ca700",
            
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  "doi": "10.35097/1563",
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  "doi": "10.35097/1563",
            
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  "doi_date_published": "2023",
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  "doi_date_published": "2023",
            
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  "doi_publisher": "",
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  "doi_publisher": "",
            
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  "doi_status": "True",
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  "doi_status": "True",
            
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  "groups": [],
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  "groups": [],
            
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  "id": "29bf644e-bfcb-4a5a-97d4-835a75085376",
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  "id": "29bf644e-bfcb-4a5a-97d4-835a75085376",
            
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  "isopen": false,
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  "isopen": false,
            
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  "license_id": "CC BY-NC-SA 4.0 
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  "license_id": "CC BY-NC-SA 4.0 
            
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Attribution-NonCommercial-ShareAlike",
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Attribution-NonCommercial-ShareAlike",
            
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  "license_title": "CC BY-NC-SA 4.0 
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  "license_title": "CC BY-NC-SA 4.0 
            
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Attribution-NonCommercial-ShareAlike",
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Attribution-NonCommercial-ShareAlike",
            
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  "metadata_created": "2023-08-04T08:51:03.451181",
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  "metadata_created": "2023-08-04T08:51:03.451181",
            
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  "metadata_modified": "2023-08-04T09:04:26.235413",
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  "metadata_modified": "2023-08-04T09:31:30.944549",
            
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  "name": "rdr-doi-10-35097-1563",
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  "name": "rdr-doi-10-35097-1563",
            
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  "notes": "Abstract: This code was used for the numerical experiments 
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  "notes": "Abstract: This code was used for the numerical experiments 
            
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in the preprint (CRC Preprint 2021/12; URL: 
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in the preprint (CRC Preprint 2021/12; URL: 
            
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https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-12.pdf) and 
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https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-12.pdf) and 
            
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in the paper \"Exponential integrators for quasilinear wave-type 
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in the paper \"Exponential integrators for quasilinear wave-type 
            
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equations\" by B. D\u00f6rich and M. Hochbruck.\r\nTechnicalRemarks: 
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equations\" by B. D\u00f6rich and M. Hochbruck.\r\nTechnicalRemarks: 
            
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This program is intended to reproduce the results from the preprint 
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This program is intended to reproduce the results from the preprint 
            
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\r\n\r\n\"Exponential integrators for quasilinear wave-type 
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\r\n\r\n\"Exponential integrators for quasilinear wave-type 
            
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equations\"\r\nby Benjamin D\u00f6rich and Marlis Hochbruck\r\n\r\nThe 
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equations\"\r\nby Benjamin D\u00f6rich and Marlis Hochbruck\r\n\r\nThe 
            
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codes generates the lines in Figure 1\r\n\r\n#### 
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codes generates the lines in Figure 1\r\n\r\n#### 
            
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Requirements\r\n\r\nThe program is tested with \r\n\r\n1) Ubuntu 
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Requirements\r\n\r\nThe program is tested with \r\n\r\n1) Ubuntu 
            
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16.04.7 LTS and Python 3.7.6 and the following version of its 
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16.04.7 LTS and Python 3.7.6 and the following version of its 
            
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modules:\r\n- numpy           -   1.15.4\r\n- scipy           -   
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modules:\r\n- numpy           -   1.15.4\r\n- scipy           -   
            
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1.4.1\r\n- matplotlib      -   3.2.1\r\n- tikzplotlib     -   
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1.4.1\r\n- matplotlib      -   3.2.1\r\n- tikzplotlib     -   
            
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0.9.6\r\n- dolfin          -   2018.1.0\r\n- fenics          -   
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0.9.6\r\n- dolfin          -   2018.1.0\r\n- fenics          -   
            
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2018.1.0\r\n\r\n2) Ubuntu 18.04.5 LTS and Python 3.6.9 and the 
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2018.1.0\r\n\r\n2) Ubuntu 18.04.5 LTS and Python 3.6.9 and the 
            
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following version of its modules:\r\n\r\n- numpy           -   
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following version of its modules:\r\n\r\n- numpy           -   
            
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1.19.2\r\n- scipy           -   1.5.1\r\n- matplotlib      -   
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1.19.2\r\n- scipy           -   1.5.1\r\n- matplotlib      -   
            
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3.3.2\r\n- tikzplotlib     -   0.9.4\r\n- dolfin          -   
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3.3.2\r\n- tikzplotlib     -   0.9.4\r\n- dolfin          -   
            
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2019.2.0.dev0\r\n- fenics          -   2019.2.0.dev0\r\n\r\n#### 
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2019.2.0.dev0\r\n- fenics          -   2019.2.0.dev0\r\n\r\n#### 
            
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Figure 1\r\nIn the folder \"DoeH21_quasilinear\" open a console and 
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Figure 1\r\nIn the folder \"DoeH21_quasilinear\" open a console and 
            
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run the following commands after each other.\r\n\r\n1) Run \"python3 
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run the following commands after each other.\r\n\r\n1) Run \"python3 
            
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1_generate_initial_matrices.py\"\r\n2) Run \"python3 
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1_generate_initial_matrices.py\"\r\n2) Run \"python3 
            
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2_paper_run_reference_solution.py\"\r\n3) Run \"python3 
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2_paper_run_reference_solution.py\"\r\n3) Run \"python3 
            
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3_paper_run_Euler.py\"\r\n4) Run \"python3 
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3_paper_run_Euler.py\"\r\n4) Run \"python3 
            
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4_paper_run_midpoint.py\"\r\n\r\nAfter running the calculations, the 
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4_paper_run_midpoint.py\"\r\n\r\nAfter running the calculations, the 
            
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errors can be found in \r\nthe folder 
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errors can be found in \r\nthe folder 
            
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\"DoeH21_quasilinear/extracted_data/\".\r\n(a) settings_* contains the 
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\"DoeH21_quasilinear/extracted_data/\".\r\n(a) settings_* contains the 
            
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information of the config file\r\n(b) infos_* contains the computed 
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information of the config file\r\n(b) infos_* contains the computed 
            
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errors\r\n(c) plot_* contains a tikz-file which gives the plot for the 
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errors\r\n(c) plot_* contains a tikz-file which gives the plot for the 
            
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\r\n    Euler and the midpoint rule separately.",
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\r\n    Euler and the midpoint rule separately.",
            
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  "orcid": "0000-0001-5840-2270",
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  "orcid": "0000-0001-5840-2270",
            
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  "organization": {
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  "organization": {
            
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    "approval_status": "approved",
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    "approval_status": "approved",
            
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    "created": "2023-01-12T13:30:23.238233",
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    "created": "2023-01-12T13:30:23.238233",
            
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    "description": "RADAR (Research Data Repository) is a 
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    "description": "RADAR (Research Data Repository) is a 
            
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cross-disciplinary repository for archiving and publishing research 
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cross-disciplinary repository for archiving and publishing research 
            
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data from completed scientific studies and projects. The focus is on 
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data from completed scientific studies and projects. The focus is on 
            
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research data from subjects that do not yet have their own 
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research data from subjects that do not yet have their own 
            
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    "image_url": "radar-logo.svg",
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    "is_organization": true,
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    "name": "radar",
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    "title": "RADAR",
            
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  "private": false,
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  "private": false,
            
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  "production_year": "2021",
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  "production_year": "2021",
            
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  "publication_year": "2023",
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  "publication_year": "2023",
            
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  "publishers": [
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  "publishers": [
            
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    {
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    {
            
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      "publisher": "Karlsruhe Institute of Technology"
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      "publisher": "Karlsruhe Institute of Technology"
            
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    }
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    }
            
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  "source_metadata_created": "2023",
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  "source_metadata_created": "2023",
            
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  "source_metadata_modified": "",
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  "source_metadata_modified": "",
            
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  "state": "active",
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      "subject_area_name": "Mathematics"
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      "subject_area_name": "Mathematics"
            
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  "tags": [
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  "tags": [
            
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    {
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      "display_name": "Maxwells equations",
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      "id": "408f9606-823e-4494-9527-e10be495ea6d",
            
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      "name": "error analysis",
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      "name": "error analysis",
            
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      "state": "active",
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      "state": "active",
            
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    },
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    },
            
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    {
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    {
            
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      "display_name": "quasilinear evolution equations",
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      "display_name": "quasilinear evolution equations",
            
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      "id": "ab5df69e-9d96-4275-b687-f24f57aefcfc",
            
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      "name": "quasilinear evolution equations",
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      "name": "quasilinear evolution equations",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
            
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    },
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      "display_name": "time integration",
            
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      "id": "05c33a87-3032-479c-af53-5a6cb2b6da8d",
            
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      "name": "time integration",
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      "name": "time integration",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
            
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    },
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    },
            
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    {
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    {
            
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      "display_name": "wave equation",
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      "display_name": "wave equation",
            
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      "id": "cec2cefd-f3c3-4de9-b1d5-f680a3a88ff5",
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      "id": "cec2cefd-f3c3-4de9-b1d5-f680a3a88ff5",
            
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      "name": "wave equation",
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      "name": "wave equation",
            
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      "state": "active",
            
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    }
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    }
            
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  ],
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  ],
            
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  "title": "Numerical experiments to \"exponential integrators for 
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  "title": "Numerical experiments to \"exponential integrators for 
            
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quasilinear wave-type equations\"",
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quasilinear wave-type equations\"",
            
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  "type": "vdataset",
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  "type": "vdataset",
            
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  "url": "https://doi.org/10.35097/1563"
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  "url": "https://doi.org/10.35097/1563"
            
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}
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}