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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
中文翻译:
具有强边界层的三阶微分方程的边值问题
更新日期:2020-05-21
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