An Explicit Numerical Method for the Fractional Cable Equation

Figure 6

Numerical solution (circles) provided by our explicit method for the fractional cable equation with 𝛾₁=0.5 and 𝛾₂=0.5 after 100 timesteps when Δ𝑥=1/10, Δ𝑡=1.3×10⁻⁵, 𝐾=𝜇=1, 𝐿=5, and 𝑆=(Δ𝑡)^𝛾/(Δ𝑥)²=0.36. Note that this value is larger than the stability limit 𝑆_×=(2^𝛾2−𝜇²(Δ𝑡)^𝛾2)/(2^{2+𝛾2−𝛾1})≃0.352… provided by (3.7). The broken line is to guide the eye.