Linear θ-Method and Compact θ-Method for Generalised Reaction-Diffusion Equation with Delay

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.