An efficient numerical method for a time-fractional telegraph equation
Jian Huang1, Zhongdi Cen1, Aimin Xu1
1Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China.
Abstract:
In this paper a time-fractional telegraph equation is considered. First the time-fractional telegraph equation is transformed into an integral-differential equation with a weakly singular kernel. Then an integral-difference discretization scheme on a graded mesh is developed to approximate the integral-differential equation. The possible singularity of the exact solution is taken into account in the convergence analysis. It is proved that the scheme is second-order convergent for both the spatial discretization and the time discretization. Numerical experiments confirm the validity of the theoretical results.
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