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Asymptotic stability of numerical methods for linear delay parabolic differential equations

机译:线性时滞抛物线方程的数值方法的渐近稳定性

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This paper is concerned with the asymptotic stability property of some numerical processes by discretization of parabolic differential equations with a constant delay. These numerical processes include forward and backward Euler difference schemes and Crank-Nicolson difference scheme which are obtained by applying step-by-step methods to the resulting systems of delay differential equations. Sufficient and necessary conditions for these difference schemes to be delay-independently asymptotically stable are established. It reveals that an additional restriction on time and spatial stepsizes of the forward Euler difference scheme is required to preserve the delay-independent asymptotic stability due to the existence of the delay term. Numerical experiments have been implemented to confirm the asymptotic stability of these numerical methods.
机译:本文通过将抛物线微分方程离散化并具有恒定的延迟,来研究某些数值过程的渐近稳定性。这些数值过程包括向前和向后的Euler差分方案和Crank-Nicolson差分方案,这些方案是通过将逐步方法应用于所得的时滞微分方程组而获得的。建立了使这些差分方案独立于时滞渐近稳定的充分必要条件。结果表明,由于存在延迟项,因此需要对前欧拉差分格式的时间和空间步长进行额外限制,以保持与延迟无关的渐近稳定性。已经进行了数值实验,以确认这些数值方法的渐近稳定性。

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