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

Abstract

• A multi-term time fractional and Riesz space distributed-order wave equation is discussed. • Firstly the equation is transformed into a multi-term time-space fractional wave equation. • The equation is solved by discretising using C–N scheme and the FEM with an unstructured mesh. • Stability and convergence are investigated. • Some examples are provided to show the effectiveness and correctness of the proposed numerical method. 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.