High-order exponential integrators for the Riesz space-fractional telegraph equation

• Published in: Communications in nonlinear science & numerical simulation 2024-01, Vol.128, p.107607, Article 107607
• Main Authors: Li, Yu, Li, Boxiao
• Format: Article
• Language: English
• Subjects: Calculation of matrix functions; Exponential Runge–Kutta method; Fractional central difference scheme; Riesz space fractional telegraph equation
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2023.107607

In this paper, we study the numerical solution of a class of Riesz space fractional telegraph equation. In the spatial direction, the equations are discretized using the fractional central difference scheme, and an equivalent semi-linear form is obtained. Then, a fourth-order exponential Runge–Kutta method is chosen in the temporal direction. Moreover, an efficient method for calculating the matrix exponent and matrix φ-function is proposed by performing a series of matrix transformations on the coefficient matrix in the semi-linear form, improving the efficiency of the matrix functions calculation. Several numerical experiments show that the convergence order of the scheme is O(h2+τ4), where h is the space step and τ is the time step. The effectiveness of the scheme is also verified. •New numerical methods are proposed for Riesz space-fractional telegraph equations.•The methods convergent of order 2 in space and order 4 in time.•The matrix functions are calculated efficiently by a series of matrix transformations.