Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Table 1

Numerical values when 𝛼=0.5, 𝛼=0.75, and 𝛼=1.0 for (13).

𝑥	𝑡	𝛼=0.5		𝛼=0.75		𝛼=1.0
		𝑢ADM	𝑢MPA	𝑢ADM	𝑢MPA	𝑢ADM	𝑢MPA	𝑢Exact
0.01	0.01	0.001118860666	0.001118859998	0.7125363089×10^−21	0.7125363089×10^−21	0.00009999999987	0.0001000000000	0.0001
0.02	0.02	0.003138022015	0.003138007574	0.2579676158×10^−18	0.2579676148×10^−18	0.0003999999915	0.0004000000000	0.0004
0.03	0.03	0.005716640278	0.005716554826	0.8097412617×10^−17	0.8097412644×10^−17	0.0008999999028	0.0009000000000	0.0009
0.04	0.04	0.008727882362	0.008727584792	0.9339702880×10^−16	0.9339702881×10^−16	0.001599999454	0.001600000000	0.0016
0.05	0.05	0.01209607907	0.01209530419	0.6224118481×10^−15	0.6224118464×10^−15	0.002499997917	0.002500000000	0.0025
0.06	0.06	0.01576873408	0.01576705530	0.2931772549×10^−14	0.2931772552×10^−14	0.003599993779	0.003600000000	0.0036
0.07	0.07	0.01970633078	0.01970312778	0.1086905954×10^−13	0.1086905954×10^−13	0.004899984313	0.004900000000	0.0049
0.08	0.08	0.02387754051	0.02387197301	0.3381735603×10^−13	0.3381735608×10^−13	0.006399965047	0.006400000000	0.0064
0.09	0.09	0.02825661342	0.02824760190	0.9203528751×10^−13	0.9203528751×10^−13	0.008099929141	0.008100000000	0.0081
0.1	0.1	0.03282181204	0.03280802591	0.2253790147×10^−12	0.2253790145×10^−12	0.009999866667	0.010000000000	0.01