TITLE

EXACT DIFFERENCE SCHEMES FOR MULTIDIMENSIONAL HEAT CONDUCTION EQUATIONS

AUTHOR(S)
Lapinska-Chrzczonowicz, M.
PUB. DATE
April 2007
SOURCE
Computational Methods in Applied Mathematics;2007, Vol. 7 Issue 2, p178
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The initial boundary-value problem for the two-dimensional heat conduction equation ∂u/∂t = ∂/ ∂x1 (k1 (u)∂u/∂x1) + ∂/∂x2 (k2(u)∂u/∂x2) is considered. A new difference scheme approximating the above equation is constructed. The error of approximation of the considered scheme is O((σ - 0.5)(h1 + h2 + τ) + h² 2 + τ²), where σ is a weight. The main difference between the method proposed in the present paper and the other difference schemes is that for the traveling wave solutions u(x, t) = U (1/2a x1 + 1/2b x2 - t), 0 ≤ x1 ≤ l1, 0 ≤ x2 ≤ l2, 0 ≤ t ≤ T, the considered scheme is exact if the grid steps satisfy definite conditions γ1 = aτ/h1 = 1/2, γ2 = bτ/h2 = 1/2. The iteration method is used to solve a nonlinear difference equation.
ACCESSION #
25732575

 

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