High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: Construction and application (II)

By constructing new numerical approximation formulas for the left and right Riemann-Liouville tempered fractional derivatives of order α∈(0,1), a numerical algorithm is proposed to solve the space tempered fractional convection equation. The algorithm is shown to be unconditionally stable and convergent with order Oτ2+h2. Finally, numerical example is provided to verify the theoretical analysis.