Numerical solution of unsteady state fractional advection–dispersion equation

Figures & data

Table 1. The approximate solution, exact solution and their comparison using $T=0.4,m=4,\gamma =2,\eta =1,\Delta t=0.0005.$

x	Exact	Laguerre	Error
0	0	1.25e − 15	1.25e − 15
0.1	−4.04e − 02	−4.04e − 02	6.51e − 06
0.2	−7.19e − 02	−7.19e − 02	1.43e − 05
0.3	−9.44e − 02	−9.44e − 02	2.22e − 05
0.4	−1.08e − 01	−1.08e − 01	2.93e − 05
0.5	−1.12e − 01	−1.12e − 01	3.44e − 05
0.6	−1.08e − 01	−1.08e − 01	3.66e − 05
0.7	−9.44e − 02	−9.44e − 02	3.51e − 05
0.8	−7.19e − 02	−7.19e − 02	2.89e − 05
0.9	−4.04e − 02	−4.05e − 02	1.75e − 05
1	0	−5.28e − 09	5.28e − 09

Figure 1. Solution for $\gamma =1.5,\eta =0.5$ and t = 0.2.

Figure 2. Solution for $\gamma =1.8,\eta =0.7$ and t = 0.2.

Figure 3. Solution for $\gamma =1.9,\eta =0.9$ and t = 0.2.

Figure 4. Solution for $\gamma =1.8,\eta =1$ and t = 0.5.

Figure 5. Solution for for $\gamma =1.9,\eta =1$ and t = 0.5.

Figure 6. Solution for $\gamma =2,\eta =0.9$ and t = 0.4.

Figure 7. Solution for $\gamma =2,\eta =1$ and t = 0.4.

Figure 8. Solution for $\gamma =2,\eta =1$ and t = 0.4.

Figure 9. Solution for $\gamma =2,\eta =1$ and t = 0.4.

Figure 10. Solution for $\gamma =2,\eta =1$ and t = 0.4.

Table 2. The approximate solution, exact solution and their comparison using $T=0.4,m=4,\Delta t=0.0005.$

x	Exact	Laguerre	Error
0	0	3e − 20	3.46e − 20
0.1	0.008	0.008	6.59e − 06
0.2	0.014	0.014	1.08e − 05
0.3	0.019	0.019	1.32e − 05
0.4	0.022	0.022	1.39e − 05
0.5	0.023	0.022	1.33e − 05
0.6	0.022	0.022	1.16e − 05
0.7	0.019	0.019	9.25e − 06
0.8	0.014	0.014	6.35e − 06
0.9	0.008	0.008	3.19e − 06
1	0	1e − 09	1.36e − 09

Figure 11. Solution for $\alpha =1.8,\beta =0.9$ and t = 0.4.