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Numerical solution of the heat equation with nonlinear boundary conditions in unbounded domains
Author(s) -
Koleva Miglena,
Vulkov Lubin
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20183
Subject(s) - mathematics , discretization , partial differential equation , finite element method , backward euler method , boundary value problem , nonlinear system , mathematical analysis , space (punctuation) , boundary (topology) , numerical analysis , euler's formula , semi infinite , method of lines , differential equation , ordinary differential equation , computer science , differential algebraic equation , physics , quantum mechanics , thermodynamics , operating system
The numerical solution of the heat equation in unbounded domains (for a 1D problem‐semi‐infinite line and for a 2D one semi‐infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi‐discretization by finite element method and the full approximation by the implicit‐explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 379–399, 2007