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On the combination of some semi‐discretization methods and boundary integral equations for the numerical solution of initial boundary value problems
Author(s) -
Chapko R.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<424::aid-pamm424>3.0.co;2-f
Subject(s) - mathematics , mathematical analysis , neumann boundary condition , boundary value problem , mixed boundary condition , discretization , integral equation , dirichlet boundary condition , singular boundary method , robin boundary condition , cauchy boundary condition , helmholtz equation , free boundary problem , poincaré–steklov operator , boundary element method , finite element method , physics , thermodynamics
We consider initial boundary value problems for the homogeneous differential equation of hyperbolic or parabolic type in the unbounded two‐ or three‐dimensional spatial domain with the homogeneous initial conditions and with Dirichlet or Neumann boundary condition. The numerical solution is realized in two steps. At first using the Laguerre transformation or Rothe's method with respect to the time variable the non‐stationary problem is reduced to the sequence of boundary value problems for the non‐homogeneous Helmholtz equation. Further we construct the special integral representation for solutions and obtain the sequence of boundary integral equations (without volume integrals). For the full‐discretization of integral equations we propose some projection methods.