@inproceedings{0a8fb9592c114d07afa8d681a01cfdc9,

title = "On numerical solution to the Cauchy-Dirichlet problem for the heat equation",

abstract = "The Cauchy-Dirichlet problem for the homogeneous heat equation in a cylinder with a non-homogeneous Dirichlet boundary condition and homogeneous initial (Cauchy) condition is under consideration. The problem is reduced to an integral equation of the first kind generated by the volume potential with a density supported in an arbitrarily thin exterior lateral boundary layer. An approximate solution to the integral equation leads to a rather simple numerical algorithm which can be called boundary layer elements by an analogy of the boundary element method. Due to the fact of the thin boundary layer as well as of a lower block triangularity of the corresponding linear system, the 3D Cauchy-Dirichlet problem (with three spatial variables) can be solved even by usual PC.",

keywords = "Boundary layer element, Cauchy-Dirichlet problem, Heat equation, Numerical solution, Volume potential",

author = "Kozhevnikov, {Alexander N.}",

year = "2007",

language = "English",

isbn = "9789889867140",

series = "Lecture Notes in Engineering and Computer Science",

pages = "605--608",

booktitle = "IMECS 2007 - International MultiConference of Engineers and Computer Scientists 2007",

note = "International MultiConference of Engineers and Computer Scientists 2007, IMECS 2007 ; Conference date: 21-03-2007 Through 23-03-2007",

}