Abstract
This paper is concerned with the analysis of the linear θ-method and compact θ-method for solving delay reaction-diffusion equation. Solvability, consistence, stability, and convergence of the two methods are studied. When θ∈[0,1/2), sufficient and necessary conditions are given to show that the two methods are asymptotically stable. When θ∈[1/2,1], the two methods are proven to be unconditionally asymptotically stable. Finally, several examples are carried out to confirm the theoretical results.
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