Fourth-Order Compact Schemes for Solving Multidimensional Heat Problems with Neumann Boundary Conditions

In this article, two sets of fourth-order compact finite difference schemes are constructed for solving heatconducting 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 problemwith Neumann boundary conditions, NumericalMethods 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 24: 165–178, 2008