求解奇异摄动抛物型时滞偏微分方程的拟合数值格式

IF 0.7 Q2 MATHEMATICS Tamkang Journal of Mathematics Pub Date : 2021-03-22 DOI:10.5556/J.TKJM.53.2022.3638
G. Duressa, M. Woldaregay
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引用次数: 11

摘要

本文给出了求解空间变量上具有小时滞的奇摄动抛物型时滞偏微分方程的指数拟合有限差分格式。用泰勒级数近似逼近含时滞项。所得的奇异摄动抛物型偏微分方程在时间离散中采用隐式欧拉法处理,在空间离散中采用指数拟合算子有限差分法处理。进行了参数一致收敛分析,收敛阶为1。通过算例和数值结果验证了该方案的理论分析。
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Fitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations
In this paper, exponentially fitted finite difference scheme is developed for solving singularly perturbed parabolic delay partial differential equations having small delay on the spatial variable. The term with the delay is approximated using Taylor series approximation. The resulting singularly perturbed parabolic partial differential equation is treated using implicit Euler method in the temporal discretization with exponentially fitted operator finite difference method in the spatial discretization. The parameter uniform convergence analysis has been carried out with the order of convergence one. Test examples and numerical results are considered to validate the theoretical analysis of the scheme.
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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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