The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory
The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory
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DOI：
10.1080/00207160.2017.1347259
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发表时间：
2018-10
影响因子：
1.8
通讯作者：
Haixiang Zhang;Xuehua Yang
中科院分区：
文献类型：
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作者：
Haixiang Zhang;Xuehua Yang
摘要针对一类带记忆的偏微分方程，提出了具有时间和空间阶截断误差的二阶向后微分公式（BDF）正交样条配置（OSC）方法。证明了BDF OSC方法在新范数下的稳定性和收敛性。此外，我们提供了三个数值实验来验证理论分析的结果，并显示BDF OSC方法的准确性和有效性。数值实验也显示了最佳的误差估计，和-范数。
ABSTRACT In this paper, a second-order backward differentiation formula (BDF) orthogonal spline collocation (OSC) method with the truncation error of order in time and in space is presented for a kind of partial differential equation (PDE) with memory. The stability and convergence of the BDF OSC method in a new norm are proved. Besides, we provide three numerical experiments to demonstrate the results of theoretical analysis and show the accuracy and effectiveness of the BDF OSC method. Numerical experiments also exhibit the optimal error estimates in the , and -norms.