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{
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{
            
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  "author": "Carle, Constantin",
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  "author": "Carle, Constantin",
            
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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": "10.35097/1512",
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  "doi": "10.35097/1512",
            
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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": "c72d6678-af20-451d-a32d-2ab91a8f1f83",
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  "id": "c72d6678-af20-451d-a32d-2ab91a8f1f83",
            
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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": "2023-08-04T08:50:57.356713",
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  "metadata_created": "2023-08-04T08:50:57.356713",
            
t
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  "metadata_modified": "2023-08-04T08:52:08.098030",
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  "metadata_modified": "2023-08-04T08:53:41.456919",
            
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  "name": "rdr-doi-10-35097-1512",
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  "name": "rdr-doi-10-35097-1512",
            
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  "notes": "Abstract: This code was used for the numerical experiments 
19
  "notes": "Abstract: This code was used for the numerical experiments 
            
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in the preprint (CRC Preprint 2021/26; URL: 
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in the preprint (CRC Preprint 2021/26; URL: 
            
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https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-26.pdf) and 
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https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-26.pdf) and 
            
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in the paper \"Error analysis of multirate leapfrog-type methods for 
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in the paper \"Error analysis of multirate leapfrog-type methods for 
            
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second-order semilinear odes\" by C. Carle and M. 
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second-order semilinear odes\" by C. Carle and M. 
            
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Hochbruck.\r\nTechnicalRemarks: The scripts inside the subfolders are 
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Hochbruck.\r\nTechnicalRemarks: The scripts inside the subfolders are 
            
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intended to reproduce the figures from the \r\npreprint \r\n> Error 
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intended to reproduce the figures from the \r\npreprint \r\n> Error 
            
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analysis of multirate leapfrog-type methods for second-order 
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analysis of multirate leapfrog-type methods for second-order 
            
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semilinear ODEs\r\n\r\nby Constantin carle and Marlis 
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semilinear ODEs\r\n\r\nby Constantin carle and Marlis 
            
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Hochbruck\r\n\r\n### Requirements\r\n\r\nThe codes are tested with 
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Hochbruck\r\n\r\n### Requirements\r\n\r\nThe codes are tested with 
            
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\r\n\r\nUbuntu 20.04.2 LTS and Python 3.8.5 and the following version 
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\r\n\r\nUbuntu 20.04.2 LTS and Python 3.8.5 and the following version 
            
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of its modules:\r\n\r\n- numpy           -   1.17.4\r\n- scipy           
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of its modules:\r\n\r\n- numpy           -   1.17.4\r\n- scipy           
            
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-   1.3.3 \r\n- dolfin (fenics) -   2019.2.0.dev0 (including mshr) 
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-   1.3.3 \r\n- dolfin (fenics) -   2019.2.0.dev0 (including mshr) 
            
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\r\n- matplotlib      -   3.1.2\r\n- tikzplotlib     -   
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\r\n- matplotlib      -   3.1.2\r\n- tikzplotlib     -   
            
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0.9.6\r\n\r\n### Generation of figures\r\n\r\nIn the folder 
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0.9.6\r\n\r\n### Generation of figures\r\n\r\nIn the folder 
            
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\"code_figure_6p1-6p2\" open a console and run the commands\r\n\r\n1. 
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\"code_figure_6p1-6p2\" open a console and run the commands\r\n\r\n1. 
            
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to obatin Figure 6.1\r\n\r\n        python3 
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to obatin Figure 6.1\r\n\r\n        python3 
            
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script_figure_2dimEx.py,\r\n\r\n2. to obtain Figure 6.2(a)\r\n\r\n        
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script_figure_2dimEx.py,\r\n\r\n2. to obtain Figure 6.2(a)\r\n\r\n        
            
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python3 script_figure_FPUT_error.py\r\n\r\n3. to obtain Figure 
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python3 script_figure_FPUT_error.py\r\n\r\n3. to obtain Figure 
            
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6.2(b)\r\n\r\n        python3 
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6.2(b)\r\n\r\n        python3 
            
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script_figure_FPUT_hamiltonian.py.\r\n\r\nIn the folder 
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script_figure_FPUT_hamiltonian.py.\r\n\r\nIn the folder 
            
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\"code_figure_6p3\" open a console and run the command\r\n\r\n       
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\"code_figure_6p3\" open a console and run the command\r\n\r\n       
            
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python3 script_figure_wave-equation.py\r\n\r\nto obtain Figure 6.3(a) 
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python3 script_figure_wave-equation.py\r\n\r\nto obtain Figure 6.3(a) 
            
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and (b).\r\n\r\nAdditionally to the plots you can get the tikz-files 
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and (b).\r\n\r\nAdditionally to the plots you can get the tikz-files 
            
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which were used for generating the plots in the pdf by uncommenting 
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which were used for generating the plots in the pdf by uncommenting 
            
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the lines\r\n\r\n       #import tikzplotlib\r\n       
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the lines\r\n\r\n       #import tikzplotlib\r\n       
            
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#tikzplotlib.save(\"*****.tikz\")\r\n\r\nat the end of each of the 
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#tikzplotlib.save(\"*****.tikz\")\r\n\r\nat the end of each of the 
            
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above scripts.",
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above scripts.",
            
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  "num_tags": 9,
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  "num_tags": 9,
            
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  "orcid": "",
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  "orcid": "",
            
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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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discipline-specific infrastructures for research data management. ",
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discipline-specific infrastructures for research data management. ",
            
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    "image_url": "radar-logo.svg",
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    "image_url": "radar-logo.svg",
            
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    "is_organization": true,
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    "is_organization": true,
            
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    "name": "radar",
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    "title": "RADAR",
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    "title": "RADAR",
            
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    "type": "organization"
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    "type": "organization"
            
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  "owner_org": "013c89a9-383c-4200-8baa-0f78bf1d91f9",
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  "owner_org": "013c89a9-383c-4200-8baa-0f78bf1d91f9",
            
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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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  ],
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  ],
            
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  "relationships_as_subject": [],
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  "repository_name": "RADAR (Research Data Repository)",
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  "repository_name": "RADAR (Research Data Repository)",
            
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  "resources": [],
            
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  "services_used_list": "",
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  "services_used_list": "",
            
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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_additional": "",
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      "subject_area_additional": "",
            
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      "subject_area_name": "Mathematics"
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      "subject_area_name": "Mathematics"
            
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    }
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    }
            
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  ],
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  ],
            
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  "tags": [
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  "tags": [
            
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    {
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    {
            
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      "display_name": "CFL condition",
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      "display_name": "CFL condition",
            
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      "id": "1b514a01-be77-4cbd-9128-0e7ef27faafe",
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      "id": "1b514a01-be77-4cbd-9128-0e7ef27faafe",
            
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      "name": "CFL condition",
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      "name": "CFL condition",
            
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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": "Chebyshev polynomials",
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      "display_name": "Chebyshev polynomials",
            
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      "id": "14f029e3-2f69-47ae-83d3-ea5a865e1e1c",
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      "id": "14f029e3-2f69-47ae-83d3-ea5a865e1e1c",
            
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      "name": "Chebyshev polynomials",
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      "name": "Chebyshev polynomials",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
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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": "Hamiltonian systems",
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      "display_name": "Hamiltonian systems",
            
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      "id": "73fdcd90-0a95-4997-af0e-b5655c43cbc4",
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      "id": "73fdcd90-0a95-4997-af0e-b5655c43cbc4",
            
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      "name": "Hamiltonian systems",
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      "name": "Hamiltonian systems",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
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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": "error analysis",
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      "display_name": "error analysis",
            
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      "id": "408f9606-823e-4494-9527-e10be495ea6d",
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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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      "vocabulary_id": null
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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": "leapfrog method",
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      "display_name": "leapfrog method",
            
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      "id": "bd9eba89-751f-4d86-a18f-162fb28d8bcf",
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      "id": "bd9eba89-751f-4d86-a18f-162fb28d8bcf",
            
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      "name": "leapfrog method",
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      "name": "leapfrog method",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
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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": "second-order ode",
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      "display_name": "second-order ode",
            
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      "id": "c2f947e8-f701-4a4d-8167-9711f8215ef0",
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      "id": "c2f947e8-f701-4a4d-8167-9711f8215ef0",
            
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      "name": "second-order ode",
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      "name": "second-order ode",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
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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": "stability analysis",
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      "display_name": "stability analysis",
            
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      "id": "28c0559e-1d3c-4fea-81c4-d79e5f5149a4",
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      "id": "28c0559e-1d3c-4fea-81c4-d79e5f5149a4",
            
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      "name": "stability analysis",
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      "name": "stability analysis",
            
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      "state": "active",
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      "state": "active",
            
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      "vocabulary_id": null
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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": "time integration",
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      "display_name": "time integration",
            
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      "id": "05c33a87-3032-479c-af53-5a6cb2b6da8d",
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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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      "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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      "state": "active",
            
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      "vocabulary_id": null
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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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  "title": "Numerical experiments to \"error analysis of multirate 
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  "title": "Numerical experiments to \"error analysis of multirate 
            
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leapfrog-type methods for second-order semilinear odes\"",
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leapfrog-type methods for second-order semilinear odes\"",
            
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  "type": "vdataset",
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  "type": "vdataset",
            
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  "url": "https://doi.org/10.35097/1512"
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  "url": "https://doi.org/10.35097/1512"
            
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}
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}