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

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

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...

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Veröffentlicht in:International journal of differential equations 2018-01, Vol.2018 (2018), p.1-13
Hauptverfasser: Chen, Xiaoli, Cheng, Xiujun, Wang, Qiong, Wu, Fengyan
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Asymptotic methods
Computational mathematics
Delay
Eigenvalues
Mathematical models
Methods
Numerical analysis
Partial differential equations
Reaction-diffusion equations
Researchers
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Zusammenfassung: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.
ISSN:1687-9643
1687-9651
DOI:10.1155/2018/6402576