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A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction–convection–diffusion systems with two small parameters and discontinuous source terms
Journal of Mathematical Chemistry ( IF 1.7 ) Pub Date : 2019-12-09 , DOI: 10.1007/s10910-019-01094-1 K. Aarthika , V. Shanthi , Higinio Ramos
Journal of Mathematical Chemistry ( IF 1.7 ) Pub Date : 2019-12-09 , DOI: 10.1007/s10910-019-01094-1 K. Aarthika , V. Shanthi , Higinio Ramos
This paper aims at solving numerically the 1-D weakly coupled system of singularly perturbed reaction–convection–diffusion partial differential equations with two small parameters and discontinuous source terms. Boundary and interior layers appear in the solutions of the problem for sufficiently small values of the perturbation parameters. A numerical algorithm based on finite difference operators and an appropriate piecewise uniform mesh is constructed and its characteristics are analyzed. The method is confirmed to reach almost first order convergence, independently of the values of the perturbation parameters. Some numerical experiments are presented, which serve to illustrate the theoretical results.
中文翻译:
求解具有两个小参数和不连续源项的奇异扰动一维抛物线反应-对流-扩散系统的非均匀差分方案
本文旨在数值求解具有两个小参数和不连续源项的奇异摄动反应-对流-扩散偏微分方程的一维弱耦合系统。对于足够小的扰动参数值,边界层和内部层出现在问题的解决方案中。构建了一种基于有限差分算子和合适的分段均匀网格的数值算法,并分析了其特性。该方法被证实几乎达到一阶收敛,与微扰参数的值无关。给出了一些数值实验,用于说明理论结果。
更新日期:2019-12-09
中文翻译:
求解具有两个小参数和不连续源项的奇异扰动一维抛物线反应-对流-扩散系统的非均匀差分方案
本文旨在数值求解具有两个小参数和不连续源项的奇异摄动反应-对流-扩散偏微分方程的一维弱耦合系统。对于足够小的扰动参数值,边界层和内部层出现在问题的解决方案中。构建了一种基于有限差分算子和合适的分段均匀网格的数值算法,并分析了其特性。该方法被证实几乎达到一阶收敛,与微扰参数的值无关。给出了一些数值实验,用于说明理论结果。