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Exact and numerical stability analysis of reaction-diffusion equations with distributed delays

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Abstract

This paper is concerned with the stability analysis of the exact and numerical solutions of the reaction-diffusion equations with distributed delays. This kind of partial integro-differential equations contains time memory term and delay parameter in the reaction term. Asymptotic stability and dissipativity of the equations with respect to perturbations of the initial condition are obtained. Moreover, the fully discrete approximation of the equations is given. We prove that the one-leg θ-method preserves stability and dissipativity of the underlying equations. Numerical example verifies the efficiency of the obtained method and the validity of the theoretical results.

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  1. School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, China

    Gengen Zhang & Aiguo Xiao

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  1. Gengen Zhang
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  2. Aiguo Xiao
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Correspondence to Aiguo Xiao.

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Zhang, G., Xiao, A. Exact and numerical stability analysis of reaction-diffusion equations with distributed delays. Front. Math. China 11, 189–205 (2016). https://doi.org/10.1007/s11464-015-0506-7

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