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Fourth-order compact schemes for solving multidimensional heat problems with Neumann boundary conditions. (English) Zbl 1185.65157
Summary: 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 [J. Zhao et al., Numer. Methods Partial Differ. Equations 23, No. 5, 949–959 (2007; Zbl 1132.65083)] 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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