  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.
