231920.fig.005
Figure 5: Exact solution (lines) and numerical solution (symbols) provided by our method for the fractional cable equation with 𝛾 1 = 0 . 5 and 𝛾 2 = 0 . 5 for different numbers of timesteps when Δ 𝑥 = 1 / 1 0 , Δ 𝑡 = 1 0 5 , 𝐾 = 𝜇 = 1 , 𝐿 = 5 , and 𝑆 = ( Δ 𝑡 ) 𝛾 1 / ( Δ 𝑥 ) 2 = 0 . 3 1 6 . This case is inside the stability region because 𝑆 is smaller 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 inset shows the results on logarithmic scale.