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- Title
Numerical analysis of temporal second‐order accurate scheme for the abstract Volterra integrodifferential equation.
- Authors
Huang, Qiong; Bi, Wenbin; Cui, Hongxin; Guo, Tao
- Abstract
In this paper, a second‐order accurate scheme is considered for the temporal discretization of the abstract Volterra integrodifferential equation with a weakly singular kernel. The time discrete scheme is constructed by the Crank–Nicolson method for approximating the time derivative and product integration (PI) rule for approximating the integral term. The proposed scheme employs a graded mesh for time to compensate for the singular behavior of the exact solution at t=0$$ t=0 $$. Under the suitable assumptions, the stability and convergence are established by the energy argument, and the error is of order k2$$ {k}^2 $$, where k$$ k $$ is the parameter for the time grids. Numerical experiments validate the theoretical estimate.
- Subjects
VOLTERRA equations; INTEGRO-differential equations; NUMERICAL analysis; CRANK-nicolson method
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 4, p2966
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9788