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Zbl 1167.65423
Mart{\'\i}n-Vaquero, J.; Vigo-Aguiar, J.
On the numerical solution of the heat conduction equations subject to nonlocal conditions. (English)
[J] Appl. Numer. Math. 59, No. 10, 2507-2514 (2009). ISSN 0168-9274

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 [the authors, Appl. Numer. Math. 59, No.~6, 1258--1264 (2009; Zbl 1167.65422)] (and this algorithm improved the results obtained with BTCS, FTCS or Dufort-Frankel three-level techniques previously used in other works, see [{\it M. Dehghan}, Appl. Numer. Math. 52, No.~1, 39--62 (2005; Zbl 1063.65079)]) with this kind of problems. Other methods got second or fourth order only when $k=sh^{2}$, while the new codes got $n$th order for $k=h$; therefore, the new schemes require a smaller storage and CPU time employed than other algorithms. We study the convergence of the new algorithms and finally compare the efficiency of the new methods with some well-known numerical examples.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)

Keywords: nonclassic boundary value problems; implicit techniques; convergence; numerical examples

Citations: Zbl 1167.65422; Zbl 1063.65079

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