A Numerical Patching Technique for Singularly Perturbed Nonlinear Differential-Difference Equations with a Negative Shift

IF 1.2 Q2 MATHEMATICS, APPLIED
R. Rao, P. Chakravarthy
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引用次数: 3

Abstract

In this paper, we present a numerical patching technique for solving singularly perturbed nonlinear differen- tial-difference equation with a small negative shift. The nonlinear problem is converted into a sequence of linear problems by quasilinearization process. After linearization, it is divided into two problems, namely inner region problem and outer region problem. The boundary condition at the cutting point is obtained from the theory of singular perturbations. Using stretching transformation, a modified inner region problem is constructed and is solved by using the upwind finite difference scheme. The outer region problem is solved by a Taylor polynomial approach. We combine the solutions of both problems to obtain an approximate solution of the original problem. The proposed method is iterative on the cutting point. The process is repeated for various choices of the cutting point, until the solution profiles stabilize. Some numerical examples have been solved to demonstrate the applicability of the method. The method is analyzed for stability and convergence.
奇异摄动非线性负移微分-差分方程的数值补片技术
本文给出了一种求解具有小负位移的奇摄动非线性微分-差分方程的数值补片技术。通过拟线性化处理,将非线性问题转化为一系列线性问题。线性化后分为内区问题和外区问题。切点处的边界条件由奇异摄动理论得到。利用拉伸变换构造了一个改进的内区域问题,并利用迎风有限差分格式求解。外区域问题采用泰勒多项式方法求解。我们把两个问题的解结合起来,得到原问题的近似解。该方法在切点上迭代。对于各种切割点的选择,重复该过程,直到溶液轮廓稳定。算例表明了该方法的适用性。分析了该方法的稳定性和收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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