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A second order numerical method for singularly perturbed delay parabolic partial differential equation

机译：奇摄动时滞抛物型偏微分方程的二阶数值方法

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Purpose The purpose of this paper is to provide a robust second-order numerical scheme for singularly perturbed delay parabolic convection-diffusion initial boundary value problem. Design/methodology/approach For the parabolic convection-diffusion initial boundary value problem, the authors solve the problem numerically by discretizing the domain in the spatial direction using the Shishkin-type meshes (standard Shishkin mesh, Bakhvalov-Shishkin mesh) and in temporal direction using the uniform mesh. The time derivative is discretized by the implicit-trapezoidal scheme, and the spatial derivatives are discretized by the hybrid scheme, which is a combination of the midpoint upwind scheme and central difference scheme. Findings The authors find a parameter-uniform convergent scheme which is of second-order accurate globally with respect to space and time for the singularly perturbed delay parabolic convection-diffusion initial boundary value problem. Also, the Thomas algorithm is used which takes much less computational time. Originality/value A singularly perturbed delay parabolic convection-diffusion initial boundary value problem is considered. The solution of the problem possesses a regular boundary layer. The authors solve this problem numerically using a hybrid scheme. The method is parameter-uniform convergent and is of second order accurate globally with respect to space and time. Numerical results are carried out to verify the theoretical estimates.
机译：目的本文的目的是为奇异摄动时滞抛物线对流扩散初始边界值问题提供一个鲁棒的二阶数值格式。设计/方法/方法对于抛物线对流扩散初始边界值问题，作者通过使用Shishkin型网格（标准Shishkin网格，Bakhvalov-Shishkin网格）在空间方向和时间方向上离散域来数值求解该问题。使用均匀的网格。时间导数通过隐式梯形方案离散化，空间导数通过混合方案离散化，混合方案是中点迎风方案和中心差分方案的组合。结论作者找到了一个参数一致的收敛方案，该方案对于奇异摄动时滞抛物线对流扩散初始边界值问题在时间和空间方面具有全局精度。同样，使用了托马斯算法，它需要更少的计算时间。独创性/值考虑奇异摄动时滞抛物线对流扩散初始边界值问题。该问题的解决方案具有规则的边界层。作者使用混合方案在数值上解决了这个问题。该方法是参数均匀收敛的，并且相对于时间和空间具有全局二阶精度。数值结果用于验证理论估计。

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