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Compact θ-method for the generalized delay diffusion equation
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DOI：10.1016/j.amc.2017.08.033.png)
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摘要
En 中文
The generalized diffusion equation with a delay has inherent complex nature because its analytical solutions are hard to obtain. Therefore, one has to seek numerical methods, especially the high-order accurate ones, for their approximate solutions. In this paper, we have established the results of the numerical asymptotic stability of the compact theta-method for the generalized delay diffusion equation. It shows that the compact theta-method is asymptotically stable if and only if (k+r)Delta t/h(2) < 10-cos(h)/12(1+cos(h))(1-2 theta) for theta is an element of [0, 1/2) and is unconditionally asymptotically stable for theta is an element of[1/2, 1], respectively. The convergent results in the maximum norm are studied according to the consistency analysis and Lax theorem. In the end, a series of numerical tests on stability and convergence are carried out to support our theoretical results. (C) 2017 Elsevier Inc. All rights reserved.
Keyword:
The compact theta-method
Generalized diffusion equation with delay
Consistency
Solvability
Asymptotic stability
Convergence
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3.4
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2.3W
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3.5W
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