Improved Accuracy Estimates of the Difference Scheme for the Two-Dimensional Parabolic Equation with Regard for the Effect of Initial and Boundary Conditions

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• 作者：N. V. Mayko
• 关键词：parabolic equation ; initial–boundary ; value problem ; finite ; difference scheme ; accuracy estimate ; boundary and initial effects
• 刊名：Cybernetics and Systems Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：53
• 期：1
• 页码：83-91
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Artificial Intelligence (incl. Robotics); Processor Architectures; Software Engineering/Programming and Operating Systems;
• 出版者：Springer US
• ISSN：1573-8337
• 卷排序：53

文摘

We obtain improved accuracy estimates of the finite-difference scheme for a two-dimensional parabolic equation in a unit square, considering the effect of the Dirichlet boundary condition and the initial condition. We prove that the accuracy order is higher near the sides and the bottom of the space-time parallelepiped.