Compact θ-method for the generalized delay diffusion equation

Qifeng Zhang, Mengzhe Chen, Yinghong Xu and Dinghua Xu

Applied Mathematics and Computation, 2018, vol. 316, issue C, 357-369

Abstract: 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 θ-method for the generalized delay diffusion equation. It shows that the compact θ-method is asymptotically stable if and only if (k+r)Δth2<10−cos(h)12(1+cos(h))(1−2θ) for θ∈[0,12) and is unconditionally asymptotically stable for θ∈[12,1], 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.

Keywords: The compact θ-method; Generalized diffusion equation with delay; Consistency; Solvability; Asymptotic stability; Convergence (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:316:y:2018:i:c:p:357-369

DOI: 10.1016/j.amc.2017.08.033

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