TY  - JOUR
AU  - Zhao, Zhengang
AU  - Zheng, Yunying
AU  - Zeng, Xianglin
PY  - 2022
TI  - Finite element approximation of fractional hyperbolic integro-differential equation
JO  - AIMS Mathematics
SP  - 15348
EP  - 15369
VL  - 7
IS  - 8
AB  - In this article, we propose a Galerkin finite element method for numerically solving a type of fractional hyperbolic integro-differential equation, which can be considered as the generalization of the classical hyperbolic Volterra integro-differential equation. Along with Galerkin finite element method in spatial direction, we apply a second order symmetric difference method in time. Next we discuss the regularity analysis of the weak solution and convergence analysis of the semi-discrete scheme. Then we further study the stability analysis and the error estimation of the fully discrete problems, according to the properties of fractional Ritz-Volterra projection, Ritz projection and so on. Numerical examples with comparisons among the proposed schemes verify our theoretical analyses.
UR  - https://doi.org/10.3934/math.2022841
DO  - 10.3934/math.2022841