A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations

Kalaiselvan Saravana Sankar; Miller John J.H.; Sigamani Valarmathi

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A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations

机译：一种均匀拟合网格方法，用于两个奇异扰动对流扩散方程的弱耦合系统

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In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection-diffusion type is considered on the interval [0, 1]. The components of the solution of this system exhibit boundary layers at 0. A numerical method composed of an upwind finite difference scheme applied on a piecewise uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. Numerical examples are provided in support of the theory.

机译：在本文中，在间隔[0,1]的情况下，考虑了对对流扩散类型的两个二阶常微分方程的奇异扰动线性系统的边值问题。该系统的解决方案的组件呈现边界层。建议在分段均匀的Shishkin网上施加在分段均匀的Shishkin网上构成的数值方法来解决问题。该方法被证明是在扰动参数中均匀的最大规范中的第一订单会聚。提供了数字示例，以支持该理论。

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《Mathematical communications》 |2019年第2期|共18页
作者
Kalaiselvan Saravana Sankar; Miller John J.H.; Sigamani Valarmathi;
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Singular perturbation problemsSystem of convection-diffusion equationsBoundary layersShishkin meshParameter uniform convergence;

机译：对流扩散方程式奇异扰动问题界面层子纹理层均匀收敛;

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1. A parameter-uniform second order numerical method for a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous convection coefficients and source terms [J] . Pathan Mahabub Basha, Vembu Shanthi Calcolo . 2017,第3期

机译：具有不连续对流系数和源术语的单个扰动对流扩散方程的弱耦合系统的参数均匀二阶数值方法
2. Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations [J] . Li-Bin Liu, Guangqing Long, Yong Zhang Advances in Difference Equations . 2018,第1期

机译：两个耦合奇摄动抛物线对流-扩散方程组的参数统一数值方法
3. PARAMETER-UNIFORM FINITE DIFFERENCE SCHEME FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS [J] . CEN Zhongdi Journal of Systems Science and Complexity . 2005,第4期

机译：耦合奇摄动对流扩散方程组的参数一致有限差分格式
4. Parameter uniform numerical method for a weakly coupled system of second order singularly perturbed turning point problem with Robin boundary conditions [C] . N. Geetha, A. Tamilselvan International Conference on Computational Heat and Mass Transfer . 2016

机译：罗宾边界条件的二阶奇异扰动转弯点问题弱耦合系统的参数均匀数值方法
5. A new stability method for singularly perturbed convection-diffusion equations. [D] . Ramakkagari, Viswanath. 2007

机译：奇摄动对流扩散方程的一种新的稳定性方法。
6. Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations [O] . Gabil M. Amiraliyev, Aysenur Ucar 2013

机译：奇摄动常微分方程时间周期解的渐近界
7. Fitted mesh method for a weakly coupled system of singularly perturbed reaction–convection–diffusion problems with discontinuous source term [O] . Mahabub Basha Pathan, Shanthi Vembu 2016

机译：具有不连续源项的奇摄动反应-对流-扩散问题的弱耦合系统的拟合网格方法

A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations

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