Year: 2008
Author: Magdalena Lapinska-Chrzczonowicz, Piotr Matus
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 2 : pp. 303–319
Abstract
The Cauchy problem for the parabolic equation $$\frac{∂u}{∂t} =\frac{∂}{∂x} (k(x,t) \frac{∂u}{∂x}) + f(u,x,,t), x \in R, t > 0,$$ $$u(x,0) = u_0(x), x\in R,$$ is considered. Under conditions $u(x, t) = X(x)T_1(t) + T_2 (t)$, $\frac{∂u}{∂x} \neq 0$, $k(x,t)=k_1(x)k_2(t)$, $f(u,x,t) = f_1(x,t)f_2(u)$, it is shown that the above problem is equivalent to a system of two first-order ordinary differential equations for which exact difference schemes with special Steklov averaging and difference schemes with any order of approximation are constructed on the moving mesh. On the basis of this approach, the exact difference schemes are constructed also for boundary-value problems and multi-dimensional problems. Presented numerical experiments confirm the theoretical results investigated in the paper.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-IJNAM-813
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 2 : pp. 303–319
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: exact difference scheme difference scheme with an arbitrary order of accuracy parabolic equation system of ordinary differential equations.