The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory
Haixiang ZhangSchool of Science, Hunan University of Technology, Zhuzhou, ChinaXuehua YangNational Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China
2017en
ABI
Аннотация
In this paper, a second-order backward differentiation formula (BDF) orthogonal spline collocation (OSC) method with the truncation error of order 32 in time and hr+1 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 L2, L∞ and H1-norms.
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