Numerical analysis of two new finite difference methods for time-fractional telegraph equation

Xiaozhong Yang, ,School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China, Xinlong Liu
2017 Discrete and continuous dynamical systems. Series B  
Fractional telegraph equations are an important class of evolution equations and have widely applications in signal analysis such as transmission and propagation of electrical signals. Aiming at the one-dimensional time-fractional telegraph equation, a class of explicit-implicit (E-I) difference methods and implicit-explicit (I-E) difference methods are proposed. The two methods are based on a combination of the classical implicit difference method and the classical explicit difference method.
more » ... nder the premise of smooth solution, theoretical analysis and numerical experiments show that the E-I and I-E difference schemes are unconditionally stable, with 2nd order spatial accuracy, 2 − α order time accuracy, and have significant time-saving, their calculation efficiency is higher than the classical implicit scheme. The research shows that the E-I and I-E difference methods constructed in this paper are effective for solving the time-fractional telegraph equation. 2020 Mathematics Subject Classification. Primary: 65M06; Secondary: 65M12.
doi:10.3934/dcdsb.2020269 fatcat:iaibusvt5rhthdbxc5dtq3tcvy