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A Closer Look at the Heat Equation

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Title: A Closer Look at the Heat Equation
Description: This compilation begins by presenting high order accurate numerical methods for solving the heat equation on general smooth regions in two dimensions. The methods use fourth order accurate techniques that the authors have developed for evaluating certain volume and surface integrals over the regions on which the differential equation is defined. In addition, the authors propose some parallel programs for solving the heat equation which have been discretized using the finite difference method. These programs have been implemented through different parallel languages such as SkelGIS library, Compute Unified Device Architecture and Streams and Iterations in Single Assignment Language. The n-dimensional heat equation is studied through the Diamond Bessel operator. The solution is found by the methods of convolution and Fourier transform in distribution theory, and the Bessel heat kernel is acquired. The closing study solves the nonlinear diamond heat equation, obtaining the solution in a compact subset and obtaining an interesting diamond heat kernel related to the nonlinear heat equation.
Authors: Márkus Oszkar
Resource Type: eBook.
Subjects: Heat equation
Categories: MATHEMATICS / Differential Equations / Partial
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 2366004
RelevancyScore: 1097
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1096.64697265625
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  Data: A Closer Look at the Heat Equation
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This compilation begins by presenting high order accurate numerical methods for solving the heat equation on general smooth regions in two dimensions. The methods use fourth order accurate techniques that the authors have developed for evaluating certain volume and surface integrals over the regions on which the differential equation is defined. In addition, the authors propose some parallel programs for solving the heat equation which have been discretized using the finite difference method. These programs have been implemented through different parallel languages such as SkelGIS library, Compute Unified Device Architecture and Streams and Iterations in Single Assignment Language. The n-dimensional heat equation is studied through the Diamond Bessel operator. The solution is found by the methods of convolution and Fourier transform in distribution theory, and the Bessel heat kernel is acquired. The closing study solves the nonlinear diamond heat equation, obtaining the solution in a compact subset and obtaining an interesting diamond heat kernel related to the nonlinear heat equation.
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  Data: <searchLink fieldCode="AR" term="%22Márkus+Oszkar%22">Márkus Oszkar</searchLink>
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  Data: eBook.
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  Data: <searchLink fieldCode="DE" term="%22Heat+equation%22">Heat equation</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Differential+Equations+%2F+Partial%22">MATHEMATICS / Differential Equations / Partial</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.353
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Heat equation
        Type: general
    Titles:
      – TitleFull: A Closer Look at the Heat Equation
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Márkus Oszkar
      – PersonEntity:
          Name:
            NameFull: Márkus Oszkar
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2020
            – D: 03
              M: 02
              Type: profile
              Y: 2023
          Identifiers:
            – Type: isbn-electronic
              Value: 9781536176360
          Titles:
            – TitleFull: A Closer Look at the Heat Equation
              Type: main
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