ABSTRACT
In this paper, we study the two-dimensional Volterra integro-differential equations for viscoelastic rods and membranes in a bounded smooth domain. The memory kernel of this equation makes it not easy to construct an efficient numerical scheme and perform theoretical analysis. The numerical method is considered by the finite difference approach for spatial discretization and Crank–Nicolson (CN) alternating direction implicit (ADI) scheme in the time direction. The integral terms are approximated by the fractional convolution quadrature. We prove that the proposed method is unconditional stable and derive error estimates in norm. The literature reported on the ADI finite difference method of this model is extremely sparse. Numerical results support the theoretical analysis.
Acknowledgments
The authors would like to thank the editor and reviewers for their constructive comments and suggestions, which helped the authors to improve the quality of the paper significantly.
Disclosure statement
No potential conflict of interest was reported by the author(s).