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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.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
Full Text: DOI
[1] Zhao, Numer Methods Partial Differential Equations
[2] and , Numerical solution of partial differential equations in science and engineering, Wiley, New York, 1982. · Zbl 0584.65056
[3] Finite difference schemes and partial differential equations, Chapman & Hall, New York, 1989. · Zbl 0681.65064
[4] Carpenter, Appl Numer Math 12 pp 55– (1993)
[5] Christie, J Comput Phys 53 pp 353– (1985)
[6] Chu, J Comput Phys 140 pp 370– (1998)
[7] Carey, Commun Numer Methods Eng 13 pp 553– (1997)
[8] Chu, J Comput Phys 148 pp 663– (1999)
[9] Dai, Numer Methods Partial Differential Equations 16 pp 441– (2000)
[10] Dai, Numer Methods Partial Differential Equations 18 pp 129– (2002)
[11] Deng, J Comput Phys 130 pp 77– (1997)
[12] Gaitonde, J Comput Phys 138 pp 617– (1997)
[13] Ge, J Comput Phys 171 pp 560– (2001)
[14] Sun, Computer Methods Appl Mech Eng 191 pp 4661– (2002)
[15] An introduction to numerical analysis, 2nd Ed, Wiley, New York, 1988.
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