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.
Acknowledgements
The authors thank the anonymous reviewers for their invaluable comments and suggestions, and thank Prof. Graeme Fairweather for stimulating discussions and for his constant encouragement and support.
Disclosure statement
No potential conflict of interest was reported by the authors.