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On the numerical solution of direct and inverse problems for the heat equation in a semi-infinite region

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
108
Identifiers
DOI: 10.1016/s0377-0427(99)00099-0
Keywords
  • Heat Equation
  • Semi-Infinite Region
  • Initial Boundary Value Problem
  • Inverse Boundary Problem
  • Green'S Function
  • Integral Equation
  • Collocation Method
  • Trigonometric Interpolation
  • Newton Method
  • Regularization

Abstract

Abstract We consider the initial boundary value problem for the heat equation in a region with infinite and finite boundaries (direct problem) and the related problem to reconstruct the finite boundary from Cauchy data on the infinite boundary (inverse problem). The numerical solution of the direct problem is realized by a boundary integral equation method. For an approximate solution of the inverse problem we use a regularized Newton method based on numerical approach for the direct problem. Numerical examples illustrating our results are presented.

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