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Fourth‐order compact schemes for solving multidimensional heat problems with Neumann boundary conditions
Author(s) -
Zhao Jennifer,
Dai Weizhong,
Zhang Suyang
Publication year - 2008
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.20255
Subject(s) - mathematics , partial differential equation , neumann boundary condition , boundary value problem , von neumann stability analysis , boundary (topology) , order (exchange) , work (physics) , von neumann architecture , mathematical analysis , pure mathematics , finance , engineering , economics , mechanical engineering
In this article, two sets of fourth‐order compact finite difference schemes are constructed for solving heat‐conducting problems of two or three dimensions, respectively. Both problems are with Neumann boundary conditions. These works are extensions of our earlier work (Zhao et al., Fourth order compact schemes of a heat conduction problem with Neumann boundary conditions, Numerical Methods Partial Differential Equations, to appear) for the one‐dimensional case. The local one‐dimensional method is employed to construct these two sets of schemes, which are proved to be globally solvable, unconditionally stable, and convergent. Numerical examples are also provided. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007