An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain |
| |
Affiliation: | 1. School of Mathematics and Statistics, Xuchang University, Xuchang, China;2. School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia;3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China;4. Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), Queensland University of Technology, Brisbane, QLD 4001, Australia |
| |
Abstract: | In this paper, the numerical analysis for a multi-term time fracstional and Riesz space distributed-order wave equation is discussed on an irregular convex domain. Firstly, the equation is transformed into a multi-term time-space fractional wave equation using the mid-point quadrature rule to approximate the distributed-order Riesz space derivative. Next, the equation is solved by discretising in time using a Crank–Nicolson scheme and in space using the finite element method (FEM) with an unstructured mesh, respectively. Furthermore, stability and convergence are investigated by introducing some important lemmas on irregular convex domain. Finally, some examples are provided to show the effectiveness and correctness of the proposed numerical method. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|