源项不连续的奇摄动Robin型边值问题的一致收敛非多项式样条方法

Q3 Mathematics
H. Debela, G. Duressa
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引用次数: 1

摘要

本文研究了一类源项不连续的二阶奇摄动常微分方程在混合型边界条件下的解。提出了一种拟合的非多项式样条方法。证明了该方法的稳定性和参数一致收敛性。为了验证该方案的适用性,考虑了两个模型问题进行数值实验,并针对不同的扰动参数值和网格大小进行了求解。数值结果按最大绝对误差和收敛速度制成表格,结果表明,对于经典数值方法不能给出好结果的地方,该方法具有更高的精度和一致收敛性,同时也改进了文献中已有方法的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Uniformly Convergent Nonpolynomial Spline Method for Singularly Perturbed Robin-Type Boundary Value Problems with Discontinuous Source Term
In this paper, a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed-type boundary conditions is considered. A fitted nonpolynomial spline method is suggested. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter, , and mesh size, The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and - uniformly convergent for where the classical numerical methods fail to give good result and it also improves the results of the methods existing in the literature.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
36
审稿时长
3.5 months
期刊介绍: Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.
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