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The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term

机译：具有不连续源项的奇摄动半线性反应扩散方程组有限差分逼近的误差分析

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We consider a coupled system of two singularly perturbed semilinear reaction-diffusion equations with a discontinuous source term. The leading term in each equation is multiplied by a small positive parameter, but these parameters have different order of magnitude. The solution of these system of equations have overlapping and interacting boundary and interior layers. Based on the discrete Green's function theory, the properties of the discretized operator are established. The error estimates are derived in the maximum norm for a central difference scheme on layer-adapted meshes, and the method is proved to be almost second order uniformly convergent independently of both the perturbation parameters. Numerical results validate the theoretical results.

机译：我们考虑两个带有不连续源项的奇异摄动半线性反应扩散方程的耦合系统。每个方程式中的首项都乘以一个小的正参数，但是这些参数具有不同的数量级。这些方程组的解具有重叠且相互作用的边界层和内部层。基于离散格林函数理论，建立了离散算子的性质。误差估计是在适用于层自适应网格上的中心差分方案的最大范数中得出的，并且证明该方法几乎是二阶均匀收敛的，而与两个扰动参数无关。数值结果验证了理论结果。

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来源
《Finite difference methods: theory and applications》|2018年|175-184|共10页
会议地点 Lozenetz(BG)
作者
S. Chandra Sekhara; Sheetal Chawla;
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作者单位

Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India;

Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India;

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原文格式 PDF
正文语种 eng
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关键词
Singular perturbation; Semilinear; Coupled system; Discontinuous source term; Uniformly convergent; Shishkin mesh; Interior layers; Discrete Green's function;

机译：奇异摄动；半线性耦合系统；不连续来源词；一致收敛； Shishkin网眼；内部层；离散格林函数;

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专利

1. Robust computational methods for a coupled system of singularly perturbed reaction-diffusion equations with discontinuous source term [J] . Mahabub Basha Pathan, Shanthi Vembu Journal of Modern Methods in Numerical Mathematics . 2015,第2期

机译：具有不连续源项的奇摄动反应扩散方程耦合系统的鲁棒计算方法
2. A FEM for a system of singularly perturbed reaction-diffusion equations with discontinuous source term [J] . Babu A.R., Ramanujam N. International journal of computational methods . 2013,第5期

机译：具有不连续源项的奇摄动反应扩散方程组的有限元
3. AN ALMOST SECOND ORDER FEM FOR A WEAKLY COUPLED SYSTEM OF TWO SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS OF REACTION-DIFFUSION TYPE WITH DISCONTINUOUS SOURCE TERM [J] . A. RAMESH BABU, N. RAMANUJAM Neural, Parallel & Scientific Computations . 2009,第2期

机译：具有连续源项的反应扩散型两个奇摄动微分方程弱耦合系统的几乎二阶有限元
4. The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term [C] . S. Chandra Sekhara Rao, Sheetal Chawla International Conference on Finite Difference Methods . 2019

机译：具有不连续源术语单个扰动半线性反应扩散方程系统的有限差分近似的误差分析
5. SINGULARLY PERTURBED SECOND ORDER DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS COEFFICIENT IN A HILBERT SPACE [D] . ZEKERIA, ABDULKENI ABDULKERIM 1984

机译：希尔伯特空间中具有不连续系数的二阶微分方程的奇摄动
6. A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces [O] . Varun Shankar, Grady B. Wright, Robert M. Kirby, -1

机译：径向基函数（RBF）-有限差分（FD）方法求解表面扩散和反应扩散方程
7. A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term [O] . Tamilselvan A., Ramanujam N., Shanthi V. 2007

机译：具有不连续源项的两个二阶常微分方程奇摄动弱耦合系统的数值方法

The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term

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