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On the numerical solution of the heat conduction equations subject to nonlocal conditions
Many physical phenomena are modelled by nonclassical parabolic boundary value problems with nonlocal boundary conditions. Many different papers studied the second-order parabolic equation, particularly the heat equation subject to the specifications of mass. In this paper, we provide a whole family...
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Published in: | Applied numerical mathematics 2009-10, Vol.59 (10), p.2507-2514 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | Many physical phenomena are modelled by nonclassical parabolic boundary value problems with nonlocal boundary conditions. Many different papers studied the second-order parabolic equation, particularly the heat equation subject to the specifications of mass. In this paper, we provide a whole family of new algorithms that improve the CPU time and accuracy of Crandall's formula shown in [J. Martin-Vaquero, J. Vigo-Aguiar, A note on efficient techniques for the second-order parabolic equation subject to non-local conditions, Appl. Numer. Math. 59 (6) (2009) 1258–1264] (and this algorithm improved the results obtained with BTCS, FTCS or Dufort–Frankel three-level techniques previously used in other works, see [M. Dehghan, Efficient techniques for the second-order parabolic equation subject to nonlocal specifications, Appl. Numer. Math. 52 (2005) 39–62]) with this kind of problems. Other methods got second or fourth order only when
k
=
s
h
2
, while the new codes got
nth order for
k
=
h
; therefore, the new schemes require a smaller storage and CPU time employed than other algorithms. We will study the convergence of the new algorithms and finally we will compare the efficiency of the new methods with some well-known numerical examples. |
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ISSN: | 0168-9274 1873-5460 |
DOI: | 10.1016/j.apnum.2009.05.007 |