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Boundary Value Problem for a Third-Order Differential Equation with a Strong Boundary Layer
Moscow University Computational Mathematics and Cybernetics Pub Date : 2020-05-21 , DOI: 10.3103/s0278641920010057
T. Ya. Ershova

Abstract

A case is considered in which when the solution to the boundary value problem for a third-order singularly perturbed ordinary differential equation has a strong boundary layer. A difference scheme on piecewise uniform Shishkin meshes is used to solve the problem numerically. It is proved that the solution to the difference problem is reduced to solving the original problem uniformly in a small parameter with almost first order in norm \(||\cdot||_{W^{h}_{1,\infty,\varepsilon}}\). Numerical analysis fits the obtained theoretical result.


中文翻译:

具有强边界层的三阶微分方程的边值问题

摘要

考虑一种情况,其中当三阶奇摄动常微分方程的边值问题的解具有强边界层时。使用分段均匀的Shishkin网格上的差分方案来数值求解该问题。证明了差分问题的解决方案简化为以范数\(|| \ cdot || __ {W ^ {h} _ {1,\ infty, \ varepsilon}} \)。数值分析符合所获得的理论结果。
更新日期:2020-05-21
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