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首页> 外文期刊>Applied Mathematical Modelling >A finite difference method for singularly perturbed differential-difference equations with layer and oscillatory behavior
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A finite difference method for singularly perturbed differential-difference equations with layer and oscillatory behavior

机译：具有层和振动特性的奇摄动微分方程的有限差分方法

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摘要

In this paper, we present a finite difference method for singularly perturbed linear second order differential-difference equations of convection-diffusion type with a small shift, i.e., where the second order derivative is multiplied by a small parameter and the shift depends on the small parameter. Similar boundary value problems are associated with expected first-exit times of the membrane potential in models of neurons. Here, the study focuses on the effect of shift on the boundary layer behavior or oscillatory behavior of the solution via finite difference approach. An extensive amount of computational work has been carried out to demonstrate the proposed method and to show the effect of shift parameter on the boundary layer behavior and oscillatory behavior of the solution of the problem.
机译：在本文中，我们提出了一种对流扩散型小扰动奇异摄动线性二阶微分方程的有限差分方法，即二阶导数乘以一个小参数，而该偏移取决于小参数。类似的边界值问题与神经元模型中膜电位的预期首次出现时间有关。在这里，研究重点是通过有限差分法研究位移对解的边界层行为或振荡行为的影响。已经进行了大量的计算工作，以证明所提出的方法，并证明位移参数对问题解的边界层行为和振动行为的影响。

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