Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation

Table 1

The maximum error, temporal, and spatial convergence orders by difference scheme (14) for different 𝛼.

𝛼		The maximum error	Temporal convergence order	Spatial convergence order
0.1	ℎ=1/4,𝜏=1/4	0.1650	—	—
	ℎ=1/8,𝜏=1/64	0.0103	1.0004	4.0017
0.2	ℎ=1/4,𝜏=1/4	0.1526	—	—
	ℎ=1/8,𝜏=1/64	0.0095	1.0014	4.0057
0.3	ℎ=1/4,𝜏=1/4	0.1400	—	—
	ℎ=1/8,𝜏=1/64	0.0087	1.0021	4.0083
0.4	ℎ=1/4,𝜏=1/4	0.1274	—	—
	ℎ=1/8,𝜏=1/64	0.0080	0.9983	3.9932
0.5	ℎ=1/4,𝜏=1/4	0.1150	—	—
	ℎ=1/8,𝜏=1/64	0.0072	0.9994	3.9975
0.6	ℎ=1/4,𝜏=1/4	0.1027	—	—
	ℎ=1/8,𝜏=1/64	0.0065	0.9955	3.9819
0.7	ℎ=1/4,𝜏=1/4	0.0907	—	—
	ℎ=1/8,𝜏=1/64	0.0058	0.9917	3.9670
0.8	ℎ=1/4,𝜏=1/4	0.0789	—	—
	ℎ=1/8,𝜏=1/64	0.0051	0.9879	3.9515
0.9	ℎ=1/4,𝜏=1/4	0.0676	—	—
	ℎ=1/8,𝜏=1/64	0.0045	0.9773	3.9090