{"@type": "dcat:Dataset", "accessLevel": "public", "accrualPeriodicity": "irregular", "bureauCode": ["006:55"], "contactPoint": {"fn": "Alfred S. Carasso", "hasEmail": "mailto:alfred.carasso@nist.gov"}, "description": "Images and Fortran codes used to generate results in the paper \"Data Assimilation in 2D Hyperbolic/Parabolic systems using stabilized explicit finite difference scheme run backward in time\" by Alfred Carasso. . In data assimilation one is given a proposed solution to a time-dependent partial differential equation at some time T and are asked to identify an initial condition at some earlier time 0 that evolves into the given solution at time T.  In this paper an artificial example of a coupled system of three nonlinear partial differential equations generalizing 2D thermoelastic vibrations, is used to demonstrate the effectiveness, as well as the limitations, of a non-iterative direct procedure in data assimilation. Data assimilation is illustrated using 512 x 512 pixel images. Such images are associated with highly irregular non-smooth intensity data that severely challenge ill-posed reconstruction procedures.", "distribution": [{"description": "Fortran codes and image data", "downloadURL": "https://data.nist.gov/od/ds/mds2-3029/ASMECODES.zip", "mediaType": "application/zip", "title": "Codes and image data"}], "identifier": "ark:/88434/mds2-3029", "issued": "2023-06-22", "keyword": ["applied mathematical analysis"], "landingPage": "https://data.nist.gov/od/id/mds2-3029", "language": ["en"], "license": "https://www.nist.gov/open/license", "modified": "2023-06-22 00:00:00", "programCode": ["006:045"], "publisher": {"@type": "org:Organization", "name": "National Institute of Standards and Technology"}, "theme": ["Mathematics and Statistics:Mathematical knowledge management"], "title": "Software and Data Associated with Paper \"Data Assimilation in 2D Hyperbolic/Parabolic systems using stabilized explicit finite difference scheme run backward in time\"."}