Purpose

The purpose of this study is to construct and analyze a parameter uniform higher-order scheme for singularly perturbed delay parabolic problem (SPDPP) of convection-diffusion type with a multiple interior turning point.

Design/methodology/approach

The authors construct a higher-order numerical method comprised of a hybrid scheme on a generalized Shishkin mesh in space variable and the implicit Euler method on a uniform mesh in the time variable. The hybrid scheme is a combination of simple upwind scheme and the central difference scheme.

Findings

The proposed method has a convergence rate of order O(N−2L2+Δt). Further, Richardson extrapolation is used to obtain convergence rate of order two in the time variable. The hybrid scheme accompanied with extrapolation is second-order convergent in time and almost second-order convergent in space up to a logarithmic factor.

Originality/value

A class of SPDPPs of convection-diffusion type with a multiple interior turning point is studied in this paper. The exact solution of the considered class of problems exhibit two exponential boundary layers. The theoretical results are supported via conducting numerical experiments. The results obtained using the proposed scheme are also compared with the simple upwind scheme.

中文翻译：

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奇摄动时滞抛物线拐点问题的高阶格式

目的

本研究的目的是构造和分析具有多个内部转折点的对流扩散型奇摄动时滞抛物线问题（SPDPP）的参数一致高阶格式。

设计/方法/方法

作者构造了一个高阶数值方法，该方法包括在空间变量中的广义Shishkin网格上的混合方案和在时间变量中的均匀网格上的隐式Euler方法。混合方案是简单迎风方案和中央差异方案的组合。

发现

所提出的方法具有阶收敛速度 Ø（ñ-2大号2+ΔŤ）。此外，使用理查森外推法获得时间变量中二阶的收敛速度。伴随外推的混合方案在时间上是二阶收敛的，在空间上几乎是二阶收敛的，直到对数因子为止。

创意/价值

研究了一类具有多个内部转折点的对流扩散型SPDPP。所考虑的问题类别的精确解具有两个指数边界层。通过进行数值实验可以支持理论结果。使用提议的方案获得的结果也与简单的迎风方案进行了比较。