231920.fig.006
Figure 6: Numerical solution (circles) provided by our explicit method for the fractional cable equation with 𝛾 1 = 0 . 5 and 𝛾 2 = 0 . 5 after 100 timesteps when Δ 𝑥 = 1 / 1 0 , Δ 𝑡 = 1 . 3 × 1 0 5 , 𝐾 = 𝜇 = 1 , 𝐿 = 5 , and 𝑆 = ( Δ 𝑡 ) 𝛾 / ( Δ 𝑥 ) 2 = 0 . 3 6 . Note that this value is larger than the stability limit 𝑆 × = ( 2 𝛾 2 𝜇 2 ( Δ 𝑡 ) 𝛾 2 ) / ( 2 2 + 𝛾 2 𝛾 1 ) 0 . 3 5 2 provided by (3.7). The broken line is to guide the eye.