High-order fractional-compact finite difference method for Riesz spatial telegraph equation
This work provides higher-order numerical methods for solving fractional partial differential equations, which is incremental for researchers in computational mathematics.
The authors developed high-order compact finite difference schemes (up to 10th-order) for Riesz derivatives and applied a 4th-order scheme to the Riesz spatial telegraph equation, achieving 4th-order convergence in both time and space, as verified by numerical experiments.
In this paper, we establish even order compact numerical schemes (4th-order, 6th-order, 8th-order, 10th-order) for Riesz derivatives by using the symmetrical fractional centred difference operator. Then we apply the derived 4th-order algorithm to the Riesz spatial telegraph equation. We carefully study the stability and convergence by matrix method, and show that convergence orders in temporal and spatial directions are both 4th order. Numerical experiments are displayed which support the compact difference schemes for Riesz derivatives and the Riesz spatial telegraph equation.